improving the cosmic distance ladder. distance and structure of … · 2017. 10. 11. · the...

Alma Mater Studiorum

Università degli Studi di Bologna

DIPARTIMENTO DI FISICA E ASTRONOMIA

Dottorato di ricerca in AstronomiaCiclo XXVII

Improving the cosmic distance ladder.Distance and structure of the Large

Magellanic Cloud.

Dottoranda:Tatiana Muraveva

Relatore:Prof. Bruno Marano

Co–Relatori:Dott.sa Gisella Clementini

Dott.sa Marcella Marconi

Dott. Enzo Brocato

Coordinatore:

Prof. Lauro Moscardini

Esame finale anno 2014

Settore Concorsuale: 02/C1 – Astronomia, Astrofisica, Fisica della Terra e dei PianetiSettore Scientifico-Disciplinare: FIS/05 – Astronomia e Astrofisica

Contents

Introduction 1

1 The cosmological distance ladder 5

1.1 Trigonometric parallax . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Gaia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Variable stars as distance indicators . . . . . . . . . . . . . . . . . . . . . 10

1.4 Classical Cepheids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 RR Lyrae stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.1 Metal abundance of RR Lyrae stars . . . . . . . . . . . . . . . . . 15

1.5.2 MV − [Fe/H] and PLKZ relations of RR Lyrae stars . . . . . . . 19

1.6 Eclipsing binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.6.1 Classification of eclipsing binaries . . . . . . . . . . . . . . . . . . 24

1.6.2 Eclipsing binaries as distance indicators . . . . . . . . . . . . . . . 25

2 The Large Magellanic Cloud 29

2.1 Magellanic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.2 Structure of the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.3 Distance to the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4 LMC Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4.1 EROS-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4.2 OGLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4.3 VMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Classical Cepheids in the VMC tile LMC 8_3 41

3.1 EROS-2 data for candidate Classical Cepheids . . . . . . . . . . . . . . . . 41

3.2 Classification of candidate Classical Cepheids . . . . . . . . . . . . . . . . 50

i

CONTENTS

3.3 Strategy for extracting bona-fide Classical Cepheids . . . . . . . . . . . . . 52

4 Eclipsing binaries in the LMC 57

4.1 EROS-2 data for eclipsing binaries . . . . . . . . . . . . . . . . . . . . . . 57

4.2 Cross-correlation with other catalogues of eclipsing binaries in the LMC . . 59

4.3 Characteristics of eclipsing binaries with existing spectroscopy . . . . . . . 63

4.3.1 Cross-matches with the VLT-FLAMES surveys . . . . . . . . . . . 63

4.3.2 AAOmega spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 63

4.4 Classification of eclipsing binaries . . . . . . . . . . . . . . . . . . . . . . 64

4.5 Period-Luminosity relation of eclipsing binaries . . . . . . . . . . . . . . . 67

4.5.1 PL relation of eclipsing binaries from the EROS-2 sample . . . . . 67

4.5.2 PL relation of eclipsing binaries from the OGLE III catalogue . . . 69

4.6 Structure of the LMC from “hot” eclipsing binaries and Classical Cepheids 74

5 RR Lyrae stars in the VMC tile LMC 5_5 77

5.1 Data for RR Lyrae stars in the bar of the LMC . . . . . . . . . . . . . . . . 77

5.2 PLKsZ relation of RR Lyrae stars in the LMC . . . . . . . . . . . . . . . 86

5.2.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2.2 Zero-point of the PLKsZ relation . . . . . . . . . . . . . . . . . . 87

5.3 Gaia observation of RR Lyrae stars in the Milky Way . . . . . . . . . . . . 90

5.3.1 Simulated Gaia data . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.2 Simulation of the MV − [Fe/H] relation of RR Lyrae stars in the

Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 RR Lyrae stars in the VMC tile LMC 8_3 97

6.1 Classification of EROS-2 candidate RR Lyrae stars . . . . . . . . . . . . . 97

6.2 Comparison with the OGLE III catalogue . . . . . . . . . . . . . . . . . . 108

6.3 Fourier analysis of the RR Lyrae stars in tile LMC 8_3 . . . . . . . . . . . 112

6.4 Metallicity of the RR Lyrae stars in tile LMC 8_3 . . . . . . . . . . . . . . 123

6.5 Ks magnitude of the RR Lyrae stars in tile LMC 8_3 . . . . . . . . . . . . 131

6.6 Distance to the tile LMC 8_3 from RR Lyrae stars . . . . . . . . . . . . . . 140

Conclusions 145

Appendix 151

ii

CONTENTS

A Properties of the “hot” eclipsing binaries in the LMC 151

iii

Introduction

The knowledge of distances is crucially important to all branches of astronomy. In order to

measure the distances astronomers have developed a number of different techniques. Some

methods, such as the trigonometric parallax, are based on geometrical principals, others

involve the concept of distance indicators. The successions of techniques used to measure

distances to celestial objects, is called cosmological distance ladder.

The Large Magellanic Cloud (LMC) is widely considered as the first step of the cos-

mological distance ladder, since it contains many different distance indicators. An accurate

determination of the distance to the LMC allows one to calibrate these distance indicators

that are then used to measure the distance to far objects.

In standard cosmology the Universe expands uniformly according to the Hubble law

v = H0d, where v is the recession velocity of a galaxy at a distance d, and H0 is the Hubble

constant which measures the expansion rate at the current epoch. H0 sets the age of the

Universe and the size of the observable Universe. Many of the methods that are used to

measure H0 are calibrated by the distance to the LMC. The LMC is distant enough, and

its main features lie close to the plane of the sky, hence, in first approximation it could be

assumed that its stellar components are all at the same distance from us. However, the LMC

has a rather complex internal structure, that must be taken into account when pushing for

distance comparisons at a few percent level.

The main goal of this thesis is to study the distance and structure of the LMC, as traced

by different distance indicators. For these purposes three types of distance indicators were

chosen: Classical Cepheids,“hot” eclipsing binaries and RR Lyrae stars. These objects

belong to different stellar populations tracing, in turn, different sub-structures of the LMC.

The RR Lyrae stars (age ≥ 10 Gyr) are distributed smoothly and likely trace the halo of the

LMC. Classical Cepheids are young objects (age ∼50-200 Myr), mainly located in the bar

and spiral arm of the galaxy, while “hot” eclipsing binaries mainly trace the star forming

regions of the LMC. Furthermore, we have chosen these distance indicators for our study,

1

INTRODUCTION

since the calibration of their zero-points is based on fundamental geometric methods. The

ESA cornerstone mission Gaia, launched on 19 December 2013, will measure trigonometric

parallaxes for one billion stars with an accuracy of 20 micro-arcsec (µas) at V ∼ 15 mag,

and 200 µas at V ∼ 20 mag, thus will allow us to calibrate the zero-points of Classical

Cepheids, eclipsing binaries and RR Lyrae stars with an unprecedented precision. One goal

of this thesis was to check the impact of Gaia on the determination of distances with RR

Lyrae stars, based on Gaia expected performances.

In this thesis we extensively use the data of the VISTA near-infrared ESO public sur-

vey of the Magellanic Clouds system (VMC, PI M.-R. Cioni, see Cioni et al. 2011). The

determination of the distance to different tiles of the VMC survey by applying the Clas-

sical Cepheid’s period-luminosity (PLKs) and the RR Lyrae period-luminosity-metallicity

(PLKsZ) relations in the Ks passband allows us to study the structure of the LMC. We also

use in our analysis visual data of the microlensing surveys EROS (Tisserand et al., 2007)

and OGLE (Udalski et al., 1997).

Chapters 1 and 2 of the thesis provide the scientific concept of our study. In Chapter 1

we focus on the general description of the cosmological distance ladder with emphasis on

the three types of distance indicators, which were specifically analysed in this study. Chap-

ter 2 gives general information about the LMC. In Chapter 3 we provide the results of our

analysis of Classical Cepheids in the LMC. We use the visual data from the EROS-2 survey

in order to classify Classical Cepheids in the VMC tile LMC 8_3 and determine their basic

properties. These parameters will be used to derive the mean Ks magnitudes of Classical

Cepheids and to estimate the distance to this tile by applying the Classical Cepheid’s PL

relation in the Ks passband. The general strategy developed to classify candidate Classical

Cepheids from the EROS-2 survey, which will be applied to all the tiles covered only by the

EROS-2 survey, is described.

Chapter 4 presents the results of our analysis of “hot” eclipsing binaries in the LMC

observed by the EROS-2 survey. We classified them on the basis of the visual inspection

and the Fourier analysis of their light curves. We then analyse the near-infrared light curves

of the eclipsing binaries that have a counterpart in the VMC catalogue, in order to study

their PL relation and the possibility of using the PL relation to determine the distance to

the LMC.

Chapter 5 and 6 summarize the work done on the RR Lyrae stars in the VMC tiles

LMC 5_5 and 8_3. By using the VMC data for a sample of RR Lyrae stars in tile LMC

2

INTRODUCTION

5_5 we derive our own PLKsZ relation. We then apply this relation in combination with

the relations from the literature to determine the distance to tiles LMC 5_5 and 8_3. The

derived distances allow us to make preliminary conclusions about the structure of the LMC.

In order to check the impact of Gaia on the determination of the RR Lyrae PLKsZ and

MV − [Fe/H] relations we simulate Gaia parallaxes for 25 RR Lyrae stars in the Milky

Way.

In the Conclusions section we summarize the work done, whereas the Appendix con-

tains tables which are too long to be inserted in the main text of the thesis.

3

Chapter 1

The cosmological distance ladder

The cosmological distance ladder is a succession of different techniques by which as-

tronomers measure the distances to celestial objects. The cosmic distance ladder is built

by transfering geometrically measured distances to nearby stars to the far universe via mul-

tiple overlapping steps (Walker, 2012). In order to determine the distance to relatively close

objects the method of trigonometric parallax is being used. However, this geometrical

method is not applicable to derive accurate distance to the objects in other galaxies. In

order to do this one needs to apply the so-called primary distance indicators which could

be calibrated from observations in the Milky Way (MW) or from theoretical considerations

(Rowan-Robinson, 1985). After establishing the distances to nearby galaxies with primary

methods, one can apply them in order to calibrate the secondary distance indicators, which

have to be used up to distances where the Hubble Law connecting the distance to the reces-

sion velocity can be applied and cosmological parameters can be estimated.

1.1 Trigonometric parallax

The most direct distance measurement technique is the method of trigonometric parallax.

Due to the rotation of the Earth around the Sun, the position of the stars on the sky change

with season in a way that depends on the distance to the star and on its direction on the sky.

If the direction of the star lies in the plane of the Earth’s orbit, the star will appear to move

back and forth on a line in this plane by an amount of ±π, where π = re/d rad. Here d is

the distance of the star and re is the radius of the Earth’s orbit around the Sun. If the star

lies perpendicular to the plane of the Earth’s orbit, at the ecliptic pole, the star will appear

to move in a circle of angular radius π = re/d. If the star lies at ecliptic latitude be, it will

move in an eclipse of semimajor axis π = re/d and of semiminor axis π sin be. The quantity

5

1.1. TRIGONOMETRIC PARALLAX

π is called trigonometric parallax of the star, and it is usually measured in arcseconds (′′).

The distance to stars is often expressed in terms of the parallax they would give. The

unit 1 parsec (pc) is defined as the distance at which the star would give a parallax of 1

arcsec. The distance d in parsecs is therefore d = 1/π(′′).

Astronomers deal with enormous ranges of distances, so it is more convenient to use

logarithmic measurements. For this reason the so-called distance modulus is widely used to

describe the distance to the object. It is defined as:

µ = m−M = 5log(d) − 5, (1.1)

where d is the distance in pc, m is the apparent magnitude of the star, and M is the

absolute magnitude, which is the magnitude the object would have at a distance of 10 pc.

The first accurate measurements of the parallax of stars were made in 1838, when

Friedrich Wilhelm Bessel at the Königsberg Observatory in Prussia estimated π = 0′′.31±

0′′.02 for the star 61 Cygni. In 1939 Thomas Henderson found 1′′.16 ± 0′′.11 for α Cen-

tauri. Work on measuring parallaxes proceeded slowly. In 1878 parallaxes of 17 stars were

known, and by 1908 the number increased to 100. The Yale Parallax Catalog published

in 1952 (Jenkins, 1952) gives parallaxes for 5822 stars. However, for the majority of stars

the parallaxes were too small and not known accurately enough to give reliable distances.

To measure the parallaxes with a good accuracy, space telescopes are needed. That’s why

the astronomers developed a space experiment, devoted specifically to precision astrometry,

Hipparcos.

Hipparcos (High precision parallax collecting satellite) was a scientific mission of the

European Space Agency (ESA), launched in 1989 and operated until 1993. The spacecraft

was equipped with a single all-reflective, eccentric Schmidt telescope, with an aperture of

29 cm. The initial objectives of the mission were to determine parallaxes of ∼ 120000

stars to a precision of 2 milli-arcseconds (mas) for the core of the catalogue, along with the

astrometry to 10-20 mas and two-colour photometry for additional 400000 stars (the Ty-

cho experiment). An optimized scanning law allowed to cover the whole sky more or less

regularly in such a way that every object was observed from 25 to 70 times depending on

ecliptic latitude (Mignard, 1998). Regarding the photometry the number of individual ob-

servations per stars varied from 70 to 300. The resulting Hipparcos catalogue of ∼ 120000

stars with an astrometric accuracy of 1 mas or better for the brightest stars, was published

in 1997. Additionally, the lower-precision Tycho Catalogue of more than a million stars

6

CHAPTER 1. THE COSMOLOGICAL DISTANCE LADDER

was published at the same time, while the enhanced Tycho-2 Catalogue of 2.5 million stars

was published in 2000. A new reduction of the Hipparcos astrometric data was published

by van Leeuwen (2007), who claims improvement of accuracies to a factor 4 for nearly all

stars brighter than Hp=8 mag1.

More accurate trigonometric parallaxes are being obtained with the Fine Guidance Sen-

sor (FGS) instrument (Nelan, 2010) on board the Hubble Space Telescope (HST). Unfortu-

nately, the sample of objects, for which accurate HST parallaxes were obtained, is small.

The determination of unprecedentedly accurate parallaxes of a huge sample of objects is

expected with the ESA satellite Gaia (Perryman et al., 2001).

1.2 Gaia

Gaia is the ESA’s cornerstone mission launched using the Soyuz ST-B rocket from Kourou

in French Guiana on 19 December 2013. The satellite is designed to produce the most

accurate three-dimensional (3D) map of the MW to date (Perryman et al., 2001). Gaia is

located at the Lagrangian point L2 and scans the sky with two telescopes by continuously

spinning around the axis perpendicular to the two lines of sight. Each celestial object will

be observed on average 70 times during the five-year mission lifetime. Gaia will determine

the position, distance, and annual proper motion of 1 billion stars with the unprecedented

accuracy of about 20 µas at V ∼ 15 mag, and 200 µas at V ∼ 20 mag. The accuracy of

the Gaia parallaxes in comparison with Hipparcos is shown in Figure 1.1. For the brightest

objects the parallax errors are dominated by calibration errors and range from ∼ 5 to ∼ 14

µas. At the faint end the behaviour of errors as a function of V magnitude is dictated by

photon noise. As it could be seen in Fig. 1.1 at a given V magnitude, parallax accuracies

are higher for red stars. Accuracy predictions include a rough estimate of the effects of

radiation damage and a 20% margin (factor 1.2) to account for unmodelled effects. The

standard errors in position and proper motions can be derived by applying factors ∼ 0.7

and ∼ 0.5, respectively, to the parallax standard errors (Brown, 2013). Some millions of

stars will be measured by Gaia with a distance accuracy of better than 1 per cent; some 100

millions or more to better than 10 per cent.

1Hipparcos magnitude is defined by the passband of the Hipparcos main detection chain which ranges from340 to 850 nm.

7

1.2. GAIA

Figure 1.1 Accuracies of determination of parallaxes as a function of source brightness inthe V band for Gaia and for Hipparcos. Contours and dots show the Hipparcos parallaxerrors from van Leeuwen (2007). The lines show the predicted Gaia sky averaged parallaxstandard errors for an early (blue) and a late (red) spectral type star. The bands around theaverage relations reflect uncertain calibration errors at the bright side and the variation inthe sky coverage at the faint end. Figure is from Brown (2013).

8


The astrometric measurements are collected applying a wide photometric band (the Gaia

G band) which covers the range 330-1000 nm. Multi-colour photometry will be obtained for

all objects by means of low-resolution spectrophotometry. The photometric instrument con-

sists of two prisms: one is called RP for Red Photometer and covers the wavelength range

640-1000 nm, the second one, called BP (Blue Photometer), operates in the wavelength

range 330-680 nm.

Before the start of Gaia five-year science phase, the commissioning was performed. It

revealed some unexpected anomalies. One problem detected during commissioning was

associated with ice appeared on some parts of the optics, causing a temporary reduction in

transmission of the telescopes. Heating the affected optics in order to remove the ice has

largely solved this problem. Another issue is associated with “stray light”, which reaches

Gaia’s focal plane at a level higher than it was predicted before launch. This light appears to

be a mixture of light from the Sun finding its way past Gaia’s 10 m-diameter sunshield and

light from other astronomical sources. The effect on the performance of Gaia is negligible

for objects at magnitude V ∼ 15 mag and brighter, but a slight degradation in the positional

accuracy is seen for fainter stars, reaching 50% for objects at Gaia’s nominal faint limit of

V ∼ 20 mag. The phenomenon of stray light will also affect the accuracy to which stellar

brightnesses will be measured. Moreover, the impact of the stray light should be more

significant for faint stars seen by the Gaia’s Radial Velocity Spectrometer (RVS).

Further tests performed during commissioning have shown that it may be possible to

extend Gaia’s reach to stars fainter than V ∼ 20 mag, while at the bright end, software

changes make Gaia to be able to measure almost all of the brightest stars in the sky, previ-

ously considered too bright for such a sensitive system. Both of these extensions will need

further analysis before being applied. Finally, Gaia laser device called the “basic angle

monitor”, designed to measure the angle of separation between Gaia’s two telescopes to an

extremely high level of accuracy, shows that the detected variations in the basic angle are

larger than expected. These variations are caused by thermal changes in the payload as Gaia

spins. Further efforts are being made to measure and accurately calibrate the variations. Af-

ter extensive testing and analysis of the system both in space and on the ground, Gaia began

scientific operations on the 25 of July 2014.

The first intermediate catalogue of science data is expected to be released to the public in

2017. However, in the case of detection of rapidly-changing objects such as supernovae and

other transient events, open alerts are being issued as soon as possible. In fact, in September

9

1.3. VARIABLE STARS AS DISTANCE INDICATORS

2014 Gaia was announced to discover its first supernovae, Gaia14aaa in a distant galaxy.

Gaia is expected to provide a huge contribution to many fields of astronomy, such as

the structure and dynamics of the MW, stellar astrophysics, physics of the Solar system,

extragalactic astronomy and fundamental physics. Moreover, Gaia will provide valuable

samples of variable stars of nearly all types, including detached eclipsing binaries (EBs),

contact or semi-contact binaries, and pulsating stars (Paczynski, 1997). Among pulsating

stars are key distance indicators such as the Cepheids, the RR Lyrae stars and the long-

period variables (LPVs). A complete sample of objects will allow determination of the

frequency of variable objects and accurate calibration of the basic relations that allow to

use these variables as primary distance indicators (see Section 1.3). Estimated numbers

are uncertain, but suggest some 18 million variables in total, including 5 million periodic

variables, 2-3 million EBs, 2000-8000 Cepheids, 60000-240000 δ Scuti variables, 70000

RR Lyrae stars and 140000-170000 Miras (Eyer & Cuypers, 2000).

In order to investigate the performance of the Gaia satellite and the contents of the even-

tual end-of-mission catalogue, Gaia’s Data Processing and Analysis Consortium (DPAC)

has a group working on the simulation of several aspects of the Gaia mission. One major

product of this work is the Gaia Object Generator (GOG, Luri et al. 2014), designed to

simulate both individual Gaia observations and the full contents of the end-of-mission cat-

alogue. GOG includes a full mathematical description of the nominal performance of the

Gaia satellite, and is therefore capable of determining the expected precision in astrometric,

photometric and spectroscopic observations. In general, the precision depends on the ap-

parent magnitude of the star, its colour, and its sky position, which affects the number and

type of observations made (due to the Gaia scanning law). In this thesis work we use GOG

simulations in order to analyse the impact of Gaia on the determination of distances with

the RR Lyrae stars.

1.3 Variable stars as distance indicators

The trigonometric parallax is a powerful tool which allows to derive the distance by using

only geometrical principals. However, in order to determine the distance with some accu-

racy beyond ∼ 10 kpc one needs to apply indirect methods and use distance indicators.

Objects which are widely used as primary distance indicators are variable stars of differ-

ent types. A variable star is an object that shows a variation of luminosity (ranging from a

10


limit given by the instrument precision to magnitudes) within a time interval that is small

compared with the evolution time of the star.

Variable stars play a fundamental role in the context of the distance scale, since they

offer several advantages with respect to normal stars. The light variation makes the variable

stars to be more easily recognised than normal stars in the same evolutionary phase, even

when stellar crowding is significant. The most important observables of a variable star

are the period and the amplitude of the luminosity variation, that can be determined with

very high precision (the period in particular) and are both independent of uncertainties on

distance and interstellar extinction.

There are two classes of variable stars: intrinsic and extrinsic variables. The variability

of the former ones is connected with internal physical phenomena. This class of variables

includes pulsating stars and supernovae. Extrinsic variables show variability connected to

external causes and include EBs and pulsars. Among intrinsic periodic variable sources, an

important role is played by the radially pulsating variables.

Radially pulsating variable stars undergo periodic changes in radius and temperature

that are responsible for the change in luminosity. The pulsation period P is related to the

natural oscillation period of a star, which can be shown to be proportional to ρ1/2, where

ρ is the mean density of the star. This natural oscillation period is essentially the time

it would take for a star to collapse if the pressure support were suddenly removed. The

pulsation mechanism is related to variations of the opacity (the so-called κ mechanism) and

the adiabatic exponent in the ionization regions of the most abundant elements in the stellar

envelopes, namely H, He and He+, the so-called γ mechanism (Eddington 1926, Zhevakin

1953, Cox & Whitney 1958). As the driving mechanisms of pulsation are active in external

layers, the inner structure is not involved and can be neglected in pulsating models (King &

Cox 1968 and references therein). Radially pulsating stars share this driving mechanism as

demonstrated by the occurrence of the so-called instability strip, the almost vertical narrow

region in the colour-magnitude diagram (CMD) where most of the pulsators are located.

Stars in different evolutionary phases cross the instability strip at different luminosity levels

so that their observations in Galactic and extra-galactic systems allow us to trace stellar

populations of different ages. In particular: RR Lyrae stars and Type II Cepheids are the

oldest stars (age> 10 Gyr); the Anomalous Cepheids are currently thought to trace the

intermediate-age population (∼ 1-5 Gyr); the Classical Cepheids (CCs) and δ Scuti stars

are the youngest among radially pulsating variables (50-200 Myr).

11

1.4. CLASSICAL CEPHEIDS

In the following sections we will summarise the properties of some classes of variable

stars which are widely being used as distance indicators: CCs, RR Lyrae stars and EBs.

1.4 Classical Cepheids

Classical Cepheids are primary distance indicators that allow to link the local distance scale

to the cosmological distances needed to determine the Hubble constant (Clementini, 2009).

CCs are high-luminosity (−2 > MV > −7), radially pulsating variable stars, with periods

generally ranging from 1 to 100 days, and commonly associated with relatively young stellar

populations, such as those found in open clusters, disks of spiral or irregular galaxies. From

the stellar evolution point of view, these variables are intermediate-mass (3 − 12 M⊙) stars

that cross the instability strip during the core-helium burning phase. The light curve of a

CC in the LMC is presented in the left panel of Figure 1.2.

CCs are widely used as primary distance indicators because they follow a period-luminosity

(PL) relation, which is a two-dimensional projection of the higher-order period-luminosity-

colour (PLC) relation (Madore & Freedman, 2012). The PL relation was discovered by

Henrietta Swan Leavitt (1868-1921), who studied 2400 CCs, mostly located in the Small

Magellanic Cloud (SMC, Leavitt & Pickering 1912). The physical basis of the CC’s PL

relation is related to the above mentioned period-density relation coupled with the Stephan-

Boltzman law, and the assumption of the mass-luminosity (ML) relation predicted by stellar

evolution for intermediate-mass stars in the central He burning phase.

In order to estimate the slope of the PL relation, a statistically significant and homoge-

neous sample of CCs is needed. An extraordinary large amount of CCs was discovered in

the two Magellanic Clouds (MCs) by the microlensing surveys MACHO and OGLE. Udal-

ski et al. (1999) used fundamental mode pulsating CCs in the Large Magellanic and Small

Magellanic Clouds to derive the following PL relations:

V0(LMC) = −2.760logP − 17.042 (1.2)

with σ=0.159 mag

V0(SMC) = −2.760logP − 17.611 (1.3)

with σ=0.258 mag.

12


0 0.2 0.4 0.6 0.8 1

16

15.8

15.6

Figure 1.2 Left panel: Light curve of a CC in the LMC observed by the EROS-2 survey.Period, expressed in days, is from the EROS-2 catalogue. Right panel: Ks-band PL relationof CCs in the 30 Doradus field of the LMC from Ripepi et al. (2012). Black open and filledcircles show fundamental mode and first-overtone mode Cepheids, respectively. Blue filledcircles are fundamental mode CCs from Persson et al. (2004). The solid lines are least-squares fit to the data.

The derived slope is in good agreement with the slope of theoretical PL relations

computed by Caputo et al. (2000) from nonlinear convective pulsation models of CCs

(MV = −2.75logP − 1.37, σ = 0.18 mag).

The zero-point of the PL relation can be calibrated either using Galactic CCs, for which

absolute magnitudes are known from parallax measurements and/or Baade-Wesselink anal-

yses (for a general review of the method see, for example, Gautschy 1987) or, by assuming

a value for the distance to the LMC. In the latter case a robust distance determination for

the LMC is necessary. The HST Key Project (Freedman et al., 2001) used the slope of the

CC’s PL relations from Udalski et al. (1999) and a zero-point consistent with an assumed

distance modulus (m − M)0 = 18.5 mag for the LMC, to measure the distances to 31

galaxies in the range from 700 kpc to 20 Mpc. Estimated distances then served to calibrate

other, more far-reaching secondary distance indicators and to determine the Hubble constant

(Freedman et al., 2001).

Despite the fact that the CCs are successfully used to measure the distance up to 20 Mpc

or more, a number of basic questions concerning the PL relation lack an answer (Fouquè

13

1.5. RR LYRAE STARS

et al. 2003, Marconi et al. 2010). The theoretical explanation of the observational evidence

of a PL relation for CCs relies on the ML relation, which is significantly dependent on

several physical and numerical assumptions (Marconi et al., 2010). Thus, the uncertainties

of the ML relation reflect on the PLC relation’s coefficients and zero-point. Another issue

is a possible non-linearity of the PL relation and the existence of a break around 10 days

(Tammann & Reindl 2002, Tammann et al. 2002, Kanbur & Ngeow 2004, Sandage et al.

2004, Ngeow et al. 2008). Moreover, it is not definitely established whether the PL relation

is universal, and consequently, if the slope derived on the basis of LMC’s and SMC’s CCs

can be safely applied to other galaxies. In the last decades, many studies were devoted to

investigate the effect of metallicity on the coefficients of the PL relation. On the theoretical

side, linear and adiabatic models mostly suggest a negligible dependence of the CC’s PL

relations on chemical composition (Chiosi et al. 1993, Alibert et al. 1999, Saio & Gautschy

1998, Sandage 1999), while nonlinear convective pulsation models predict a significant

metallicity effect on the PL relations (Bono et al. 1999, Fiorentino et al. 2002, Marconi et

al. 2005). Some empirical studies support the nonlinear theoretical scenario (Romaniello

et al. 2005, 2008). Some of these issues can be resolved by using the PL relation in the

infrared passbands. The PL relation in the Ks passband of CCs in the LMC observed

with the near-infrared VMC survey (Cioni et al., 2011) is presented in the right panel of

Figure 1.2. It is well known that the intrinsic width of the CC’s PL relation decreases as a

function of increasing wavelength (e. g. Madore & Freedman 1991; McGonegal et al. 1982;

Caputo et al. 2000). The amplitude of pulsation in the infrared passbands is smaller than in

the visual one, so the mean magnitude could be determined more precisely. Moreover, in

the infrared bands the problem of reddening is less important and the effect of metallicity on

the PL seems to be smaller (Groenewegen & Oudmaijer 2000; Caputo et al. 2000; Marconi

et al. 2005). Therefore, the PL relation of CCs in the near-infrared passbands is a very

powerful tool to determine the distances to the LMC and other galaxies.

1.5 RR Lyrae stars

RR Lyrae stars are primary distance indicators located mainly in the halos of galaxies and

in globular clusters. RR Lyrae stars are old (age > 10 Gyr), low-mass (∼ 0.6 − 0.8 M⊙)

core-helium burning stars that lie within the instability strip on the horizontal branch (HB)

of the CMD.

14


0 0.2 0.4 0.6 0.8 1

19.5

19

18.5

18

0 0.2 0.4 0.6 0.8 1

19.5

19

18.5

Figure 1.3 Light curves of ab-type (left panel) and c-type (right panel) RR Lyrae stars ob-served by the EROS-2 survey in the LMC. Periods expressed in days are from the EROS-2catalogue.

The prototype star RR Lyrae in the constellation of Lyra was discovered in 1899 by

Williamina Fleming. In the following years a significant number of these pulsators were

observed in globular clusters by Bailey, who classified them on the basis of the period and

shape of the light curve. In particular, RR Lyrae stars were divided into ab-type (RRab),

which have asymmetric light curves, periods in the range from ∼ 0.4 to ∼ 1 day and am-

plitude in the visual band Amp(V ) steadily decreasing as the period increases, and c-type

(RRc) with amplitude ranging from 0.2 to 0.6 mag, sinusoidal shape of the light curves and

period ranging from ∼ 0.2 to ∼ 0.4 day. Examples of light curves of RRab and RRc stars

in the LMC are presented in Figure 1.3. According to the theory of stellar pulsation the

two types of RR Lyrae stars undergo pulsation in different modes. RRab stars pulsate in the

fundamental mode and RRc stars in the first-overtone mode. There is also a third type of

RR Lyrae stars, called double-mode or RRd stars, who undergo pulsation in both modes.

The RRd stars are particularly useful to obtain independent estimates of the stellar mass

(Petersen 1973; Bono et al. 1996; Bragaglia et al. 2001).

1.5.1 Metal abundance of RR Lyrae stars

The RR Lyrae stars are relatively low-mass stars, so the nucleosynthesis of significant

amount of elements heavier than carbon and oxygen is not expected during the lifetime

of these stars (Smith, 1995). Thus, the abundance of heavy elements in the atmosphere of

15

1.5. RR LYRAE STARS

the RR Lyrae stars reflects the abundance of heavy elements in the interstellar gas cloud

from which the stars were formed. This fact makes the RR Lyrae stars useful tracers of the

chemical history of the system they belong to.

In order to describe the iron (Fe) abundance of stars, the [Fe/H] notation is used. In this

notation, the ratio of Fe over hydrogen (H) in the photosphere of a star is related to that ratio

in the Sun:

[Fe/H] = log(Fe/H)star − log(Fe/H)⊙ (1.4)

The metallicity [Fe/H] of RR Lyrae stars ranges from ∼ −2.5 to ∼+0.2 dex.

The metal abundance of RR Lyrae stars is often measured with the ∆S index (Preston

1959). The spectral type of RR Lyrae stars as determined from the hydrogen Balmer lines

is generally later than the spectral type determined from the CaII K-line, and the latter

is generally weaker than expected on the basis of the Balmer line spectral classification.

Preston (1959) defined the ∆S index as the difference in tenths of spectral class between

the spectral type of a RR Lyrae at minimum light estimated from the hydrogen lines [Sp(H)]

and that estimated from the intensity of the CaII K line [Sp(K)]:

∆S = 10[Sp(H)− Sp(K)]. (1.5)

The [Fe/H] abundance is well correlated with the ∆S index, and a number of different cal-

ibrations of the ∆S index in terms of [Fe/H] abundance exist in the literature (e.g. Preston

1959; Jurcsik 1995; Gratton et al. 2004, etc.).

A few high resolution spectroscopic studies of elemental abundances of RR Lyrae stars

are also found in the literature (Butler et al. 1976, 1979; Clementini et al. 1995; Lambert

et al. 1996; Kolenberg et al. 2010; For et al. 2011; Kinman et al. 2012; Govea et al 2014,

Pancino et al. 2014, submitted to MNRAS). For variables in globular clusters, individual

metal abundances can be inferred from the accepted metallicities of the host clusters2.

Indeed, the most appropriate way to measure the metallicity of RR Lyrae stars is through

spectroscopy. Gratton et al. (2004) derived metal abundances of 98 RR Lyrae stars in the2A number of different metallicity scales exist in the literature. Among the most used ones are Zinn & West

(1984) (hereafter referred as ZW) scale which is based on a variety of integrated photometric and spectroscopicindices calibrated from the few echelle photographic spectra existing at the time; Carretta & Gratton (1997)scale which was derived from the analysis of a large sample (∼ 160) of bright giants in 24 globular clusters,whose chemical abundances were obtained from equivalent widths measured on high dispersion CCD spectra;and Carretta et al. (2009) scale (hereinafter, C09) that is based on the analysis of spectra of about 2000 redgiant branch (RGB) stars in 19 Galactic globular clusters. Specifically used for RR Lyrae stars is Jurcsik(1995) metallicity scale (hereafter referred as J95) based on both spectroscopic cluster abundances and ∆Smeasurements of cluster variables. J95 metallicity scale is valid both for globular clusters and field RR Lyrae

16


LMC from low resolution spectra by comparing the strength of the CaII K line with that of

the H lines, the derived metallicities are on a metallicity scale which is, on average, ∼ 0.06

dex more metal-rich than the Zinn & West (1984) scale.

However, when spectroscopical observations are not available or feasible, an estimate of

“photometric” metallicity could be inferred from the φ31 parameter of the Fourier decom-

position of RR Lyrae’s light curves. According to Simon & Teays (1982) the light curve of

a RR Lyrae star can be fitted with a Fourier function of the form:

m(t) = A0 +N∑

i=1

Aicos[iω0(t− t0) + φi] (1.7)

where m(t) is the star apparent magnitude at time of observation t, A0 is the average ap-

parent magnitude, N is the number of fitted terms, ω0 is the angular pulsation frequency of

the star (ω0 = 2π/P0), t0 is the time of maximum light, and Ai and φi are the amplitude

and phase coefficients of the individual Fourier terms. The shape of the light curves can be

quantified by the low order coefficients of the fit: Ri1 = Ai/A1 and φi1 = φi − iφ1. The

A1, A2 and the φ21, φ31 parameters of the Fourier decomposition can be used to classify

the RR Lyrae stars (see e.g., Simon & Teays 1982, Cacciari et al. 2005).

Jurcsik & Kovacs (1996) derived a relation between the Fourier parameter φ31 of the

V -band light curve of field ab-type RR Lyrae stars, the period and the star metallicity on

the Jurcsik (1995) metallicity scale:

[Fe/H] = −5.038 − 5.394P + 1.345φ31. (1.8)

Jurcsik & Kovacs (1996) introduced the so-called compatibility condition and defined

a deviation parameter DF :

DF = |Fobs − Fcalc|/σF , (1.9)

where Fobs is the observed value of the given Fourier parameter, Fcalc is its predicted

value from the other observed parameters, σF is the corresponding standard deviation. Dm

is the maximum of the deviation parameters {DF } and measures the regularity of the light

stars, and is related to the ∆S index through the relation:

[Fe/H]J95 = −0.190(±0.007)∆S + 0.027(±0.052) (1.6)

17

1.5. RR LYRAE STARS

curve. According to Jurcsik & Kovacs (1996) only if the light curve of the RRab star satis-

fies the compatibility condition Dm < 3 can Eq. 1.8 be used for a reliable estimate of the

star metal abundance [Fe/H]. However, Cacciari et al. (2005) adopted a relaxed compatibil-

ity condition, and found that a maximum value of 5 for Dm allows to increase the statistic

without affecting significantly the results. Kapakos et al. (2011) found that the criterion

Dm < 3 cannot lead to a robust sample of RRab stars without taking into consideration the

σDm . Thus they applied the criterion σDm < 3 and Dm − σDm < 3 in their analysis.

Morgan et al. (2007) found the relation between metallicity on the ZW metallicity scale,

φ31 and P for RRc stars:

[Fe/H]ZW = 52.466P 2 − 30.075P +0.131φ231 +0.982φ31 − 4.198φ31P +2.424 (1.10)

which has a standard deviation of 0.145 dex. Finally, Nemec et al. (2013) have derived a

new metallicity calibration of the φ31 parameter based on spectroscopic and photometric

properties of 41 RR Lyrae stars observed by the Kepler space telescope and derived P −

φ31 − [Fe/H] relations for RRab and RRc stars, separately. Since Nemec et al. (2013)

metallicity calibrations are derived using high dispersion spectra analysed with standard

reduction procedures, the derived metallicities are on the high dispersion spectroscopy scale

of Carretta et al. (2009).

For ab-type RR Lyrae stars the new calibration equation is:

[Fe/H] = b0 + b1P + b2φs31_kep+ b3φ

s31_kepP + b4(φ

s31_kep)2 (1.11)

The coefficients of equation (1.11) are: b0 = −8.65 ± 4.64, b1 = −40.12 ± 5.18, b2 =

5.96 ± 1.72, b3 = 6.27 ± 0.96, b4 = −0.72 ± 0.17, with rms of the fit of 0.084 dex. The

φs31_kep is the parameter of the sine Fourier decomposition in Kepler magnitudes which

can be derived from the φs31 in the Johnson V band by applying the equation:

φs31_kep = φs

31(V ) + (0.151 ± 0.026) (1.12)

For c-type RR Lyrae stars Nemec et al. (2013) derived the equation:

[Fe/H]C09 = b0 + b1P + b2φc31 + b3φ

c31P + b4P

2 + b5(φc31)

2 (1.13)

The coefficients of equation (1.13) are: b0 = 1.70 ± 0.82, b1 = −15.67 ± 5.38, b2 =

0.20 ± 0.21, b3 = −2.41 ± 0.62, b4 = 18.00 ± 8.70, b5 = 0.17 ± 0.04, and the rms error

of the fit was 0.13 dex. The φc31 is the parameter of the cosine Fourier decomposition in the

18


V band which could be derived from the V sine decomposition parameter by applying the

equation:

φc31 = φs

31 − π (1.14)

We will use Nemec et al. (2013) relations in 6 to derive photometric metallicities for the

RR Lyrae stars.

Di Fabrizio et al. (2005) measured photometric metallicities from the φ31 Fourier pa-

rameter for 29 LMC RRab stars and compared their values with the spectroscopic metal

abundances derived for these stars by Gratton et al. (2004). They found that the average

difference between photometric and spectroscopic metallicities is 0.30±0.07 dex, with the

photometric abundances being larger. This test provides an indication of the soundness of

photometric metallicities of RR Lyrae stars.

1.5.2 MV − [Fe/H] and PLKZ relations of RR Lyrae stars

RR Lyrae stars make useful distance indicators because of the existence of an absolute

magnitude-metallicity relation in the V band: MV − [Fe/H] (Sandage 1981a,b) and of a

period-luminosity-metallicity relation in the K band: PLKZ (Longmore et al. 1986, Bono

et al. 2003, Catelan et al. 2004, Sollima et al. 2008, and references therein).

In the past decades several authors studied the MV − [Fe/H] relation for RR Lyrae stars

using a number of methods, including synthetic Horizontal Branch models (Lee, 1994)

and the Baade-Wesselink method (Fernley et al., 1998a). Gratton et al. (2004) combined

spectroscopically determined metallicities with high accuracy photometry in the V band of

∼ 100 RR Lyrae stars in the LMC (Clementini et al., 2003) and derived the luminosity-

metallicity relation:

V0 = (0.214 ± 0.047)([Fe/H] + 1.5) + (19.064 ± 0.017), (1.15)

where V0 is the apparent dereddened average magnitude.

The slope of this relation is in a good agreement with the slope derived for the luminosity-

metallicity relation of RR Lyrae stars in the MW (Fernley et al., 1998a) and HB stars

in the globular clusters of M31 (Rich et al., 2005). This fact supports the idea that the

luminosity-metallicity relation of RR Lyrae stars is, in first approximation, linear and uni-

versal (Clementini, 2009).

The zero-point of the MV − [Fe/H] relation can be determined with a number of dif-

ferent techniques among which are: (i) the parallaxes of RR Lyrae stars in the MW; (ii)

19

1.5. RR LYRAE STARS

the calibration via globular clusters, whose distances are determined using absolute magni-

tudes of subdwarfs measured by the Hipparcos satellite; (iii) various theoretical and empir-

ical assumptions, such as the adoption of the value for the distance to the LMC. Benedict

et al. (2011) derived the zero-point MV = 0.45 ± 0.05 mag for [Fe/H]=−1.5 dex using

HST parallaxes of five MW RR Lyrae stars and adopting the slope from Gratton et al.

(2004). This value is about 0.2 mag brighter than the value of MV = 0.66 ± 0.14 mag

at [Fe/H]=−1.48 ± 0.07 derived by Catelan & Cortes (2008) for RR Lyrae itself, but has a

significantly smaller error.

There are theoretical and empirical suggestions that the MV − [Fe/H] relation is not

linear over the whole metallicity range (Marconi, 2009). The relation may also be affected

by a number of uncertain factors such as evolutionary effects, α-element enhancement, etc.

Finally, the determination of distances from analysis of field RR Lyrae stars observed in the

optical passbands depends on the reddening; this is the strongest driver for moving to the

infrared when at all possible. Three of the five galactic RR Lyrae stars with HST parallaxes

(Benedict et al., 2011) have reddening E(B−V ) ≥ 0.1 mag, so the zero-point is potentially

more robust in the infrared (Walker, 2012). The near-infrared PLKZ relation of RR Lyrae

stars has a list of other advantages in comparison with the visual MV − [Fe/H] relation.

First of all, the luminosity in the K passband is less dependent on metallicity. Moreover,

the light curves of RR Lyrae stars in the K band have smaller amplitudes and are more

symmetrical, hence the determination of the mean K magnitudes is more precise.

The near-infrared PLKZ relation of RR Lyrae stars was studied by several authors both

from a theoretical and an observational point of view. Longmore et al. (1986) pioneering

work was followed by Liu & Janes (1990), Skillen et al. (1993) and Jones et al. (1996). A

comprehensive analysis of the IR properties of RR Lyrae stars was performed by Nemec et

al. (1994).

Bono et al. (2003) derived the semi-theoretical relation:

MK = −2.101logP + (0.231 ± 0.012)[Fe/H] − (0.770 ± 0.044), (1.16)

Catelan et al. (2004) presented a theoretical calibration of the RR Lyrae PLKZ relation

based on synthetic horizontal branch models computed for several different metallicities,

fully taking into account evolutionary effects besides the effect of chemical composition.

They derived the relation:

20


Figure 1.4 PLK relation for RR Lyrae stars in the LMC cluster Reticulum. Open symbolsshow RRc stars after their periods have been fundamentalized by adding 0.127 to the loga-rithm of the period. Filled symbols are RRab stars, the line shows the theoretical predictionfrom Bono et al. (2003). Figure is from Dall’Ora et al. (2004).

MK = −2.353logP + 0.175logZ − 0.597 (1.17)

By using Eqs. 9 and 10 in Catelan et al. (2004) and assuming [α/Fe]∼ 0.3 (e.g., Carney

1996) we transformed Eq. 1.17 into the form:

MK = −2.353logP + 0.175[Fe/H] − 0.869 (1.18)

Dall’Ora et al. (2004) obtained the relation between apparent K magnitude and period

for 21 RRab and 9 RRc stars in the LMC globular cluster Reticulum.:

⟨K⟩ = (−2.16 ± 0.09)logP + (17.352 ± 0.025) (1.19)

with standard deviation of 0.03 mag.

Figure 1.4 shows the PLK relation derived by Dall’Ora et al. (2004). They used this

relation in combination with Eq. 1.16 from Bono et al. (2003) to derive (m − M)0 =

18.52±0.005(random)±0.117(systematic) mag for the distance modulus of Reticulum.

21

1.5. RR LYRAE STARS

Del Principe et al. (2006) obtained the PLKZ relation from the analysis of RR Lyrae

stars of different metallicities in the globular cluster ω Cen. Benedict et al. (2011) calibrated

the zero-point of Del Principe et al.’s relation using the HST parallaxes of five RR Lyrae stars

in the MW and obtained:

MK = (−2.71 ± 0.12)(logP + 0.28) + (0.12 ± 0.04)([Fe/H] + 1.58)

−(0.57 ± 0.02) (1.20)

Sollima et al. (2008) derived the PLKZ relation from the analysis of 544 RR Lyrae

variables in 15 Galactic clusters and in the LMC globular cluster Reticulum. Mean K

magnitudes were estimated by combining Two-Micron-All-Sky-Survey (2MASS, Cutri et

al. 2003) photometry and literature data. The zero-point was calibrated on RR Lyrae itself,

whose distance modulus was deried using the star trigonometric parallax by Benedict et al.

(2002). Sollima et al. (2008) provide the relation:

MK = (−2.38 ± 0.04)logP + (0.08 ± 0.11)[Fe/H]CG − (1.07 ± 0.11), (1.21)

where P is the fundamental-mode period, and the metallicity [Fe/H]CG is in the Carretta

& Gratton (1997) metallicity scale. By applying this relation to the K data from Dall’Ora et

al. (2004) the distance modulus of Reticulum was determined to be: (m−M)0 = 18.48±

0.11 mag (Sollima et al., 2008).

Szewczyk et al. (2008) obtained deep infrared J and K observations of five fields lo-

cated in the LMC bar. Using different theoretical and empirical PLKZ calibrations they

found the distance modulus of the LMC to be 18.58±0.03(statistical)±0.11(systematic)

mag.

Borissova et al. (2009) combined near-infrared photometry and spectroscopically mea-

sured metallicity for a sample of 50 field RR Lyrae stars in inner regions of the LMC, and

derived the relation:

MK = (−2.11 ± 0.17)logP + (0.05 ± 0.07)[Fe/H] − 1.05 (1.22)

Borissova et al. (2009) had 5 measurements in the K passband for most stars in their

sample. Templates from Jones et al. (1996) were used to fit the light curves of the RR Lyrae

stars and derive mean K magnitudes. The zero-point of the relation was calculated using

22


Figure 1.5 LogP vs. J0 and LogP vs K0 plots for field RR Lyrae stars in the LMC. As-terisks represent Szewczyk et al. (2008) data, open circles are data from Borissova et al.(2009). Solid lines show the best-fit relations obtained using only Borissova et al. (2009)data, dashed lines are for the combined samples. Figure is from Borissova et al. (2009).

the mean K magnitude, the reddening andthe trigonometric parallax of RR Lyrae itself,

from Sollima et al. (2008). By applying Eq. 1.22 Borissova et al. (2009) determined the

LMC distance modulus to be: (m−M)0 = 18.53 ± 0.13 mag.

Figure 1.5 shows the PLK relation obtained by Borissova et al. (2009) combining their

data with the data from Szewczyk et al. (2008). Comparing the PLK relation derived for

the RR Lyrae stars in the Reticulum cluster (Fig. 1.4) and to the relation for field LMC RR

Lyrae stars (Fig. 1.5) one can see that the spread is significantly smaller for the objects in the

cluster. It could be due to depth effects or, more likely, it could suggest that the metallicity

effect should be taken into account.

Metallicities in all the above relations are on, or close to the Zinn & West metallicity

scale, except for Eq. 1.21, which is on the Carretta & Gratton (1997) metallicity scale.

The PLKZ relation is a very powerful tool to measure distances. However, the PLKZ

23

1.6. ECLIPSING BINARIES

relations published in the literature often were derived from small samples of RR Lyrae

stars. Additionally, the small number of observations in the K band limited the determina-

tion of accurate mean K magnitudes. A large sample of RR Lyrae stars in the LMC with

12 or more epochs in the Ks band light curves is provided by the VMC survey (Cioni et

al., 2011). One goal of this thesis work was to derive a new PLKsZ relation based on

the VMC photometry. Another fundamental issue is the derivation of the zero-point of the

PLKZ relation. This problem will be solved when unprecedentedly accurate trigonometric

parallaxes for large numbers of RR Lyrae stars will be provided by Gaia. In this thesis we

present simulated parallaxes for bright RR Lyrae stars in the MW and use them to establish

the accuracy of the PLKZ and MV − [Fe/H] relations zero-points as it will be calibrated

with Gaia.

1.6 Eclipsing binaries

EBs are binary stars in which the orbit plane of the two stars lies nearly in the line of the

sight of the observer, so the components of the system undergo mutual eclipses. Examples

of the light curves of EBs are presented in Figure 1.6.

1.6.1 Classification of eclipsing binaries

The classification of EBs is based on the distance between components, relative to their

sizes. If the two components do not fill their Roche lobes, the system is considered to be

a detached binary. In a semi-detached binary one of the two components fills its Roche

lobe and mass transfer occurs. In contact EBs both stars fill their Roche lobes. To classify

contact and detached/semi-detached binaries analysis of the Fourier parameters and visual

inspection of the light curves are necessary.

Rucinski (1993) showed that a simple description of the light variation of binaries could

be obtained through the cosine Fourier decomposition∑

ai cos(2πiφ). In this decompo-

sition the coefficient a0 is the average magnitude of the model fit, a1 and a3 represent

the difference in depth between the two eclipses, a2 reflects the total amplitude of the bi-

nary variability and a4 is related to the eclipse “peakedness" that goes to zero for the light

curves of contact binaries. Hence, the combination of the two cosine coefficients a2 and a4

could serve as a separator of contact and non-contact (detached and semi-detached) binaries.

Namely, the curve described by the relation a4 = a2(0.125 − a2), where both coefficients

are negative, separates the regions of the contact and non-contact binaries on the a2 versus

24


lm0467n17850 P=4.324035 N=500

lm0447n7830 P=1.715561 N=490

lm0375k19793 P=2.158691 N=346

lm0366k19655 P=1.295471 N=303

lm0344m10932 P=2.077371 N=443

lm0211k9308 P=2.341696 N=420

Figure 1.6 Light curves in the REROS band of EBs observed in the LMC by the EROS-2survey. P - period (day), N - number of the observations. Figure is from Muraveva et al.(2014a).

a4 plane (Rucinski, 1993). Rucinski (1997) performed the Fourier analysis of the IC-band

light curves to extract a sample of the contact binaries from OGLE EBs in nine fields in

Baade’s Window.

However not only genuine contact binaries, but also variables with contact-like light

curves such as the ellipsoidal variables may be misclassified as contact binaries. Ellipsoidal

variability is observed in close binary systems when one or both components is (are) dis-

torted by the tidal interaction with the companion. The main reason of the variability is the

change of the projected areas on the sky because of the orbital motion of the components.

Large samples of ellipsoidal variables were published by Soszynski et al. (2004), who used

OGLE II and OGLE III photometry, and by Derekas et al. (2006), who used the MACHO

database. Since the light curves of contact binaries and non-eclipsing ellipsoidal variables

have similar shapes and could be easily mistaken, in the following analysis we adopt the

term “contact-binary-like” systems for all objects passed by the Fourier filter.

1.6.2 Eclipsing binaries as distance indicators

EBs can be used as distance indicators, since some fundamental stellar parameters can be

determined using geometrical constraints of the systems. Masses of components are esti-

25


mated dynamically via radial velocities, radii from the eclipse durations and the temperature

ratio (strictly the surface-brightness ratio) from the eclipse depths. The radii and tempera-

ture together are used to measure the luminosity of the system. From the estimated luminos-

ity and observed fluxes the distances to the EBs can be determined. This method requires

photometric and spectroscopic data (see reviews by Andersen 1991; Torres et al. 2010) and

is used to measure the distances to nearby galaxies. Recently, Pietrzynski et al. (2013) used

EBs to measure a distance to the LMC which is considered to be accurate to 2 %.

EBs may serve as distance indicators even when spectroscopy is not available. W UMa

type stars are contact binary systems with orbital periods typically less than 1 day, com-

posed of main sequence turn-off stars (Rucinski, 1998). It was shown that this class of

binaries could be used as distance indicators since the size of the two components could

be determined from the orbital period, which in combination with the colour information

allows one to derive absolute magnitudes (Rucinski 1997, and references therein). Indeed,

Rucinski (1997) used the method to determine the distance to W UMa-type contact systems

in the Galactic Bulge.

While W UMa type stars in the Galaxy seem to be limited to periods P < 1.3−1.5 day,

massive, young, blue systems of W UMa type with longer orbital periods of 2-3 day exist

in the LMC (Rucinski, 1999). These objects may follow a PL relation. Rucinski (1999)

suggested the existence of a PL relation at maximum light in the visual band (Figure 1.7),

but with a large scatter, possibly due to unaccounted effects of the interstellar extinction.

One goal of this thesis was to check the existence of the PL relation for young massive

contact EBs in the LMC and the possibility of using this relation to determine the distance

to this galaxy.

26


Figure 1.7 Relation between the orbital period and the V -magnitude at maximum light forEBs in the LMC. Different symbols mark three colour index ranges: filled circles representextra-blue binaries, open circles - red binaries, semi-filled circles are moderately-blue sys-tems (see Rucinski 1999 for details). Lines represent linear fits to the extra-blue (solid line)and moderately-blue (dashed line) subsamples. Figure is from Rucinski (1999).

27


28

Chapter 2

The Large Magellanic Cloud

2.1 Magellanic System

The Magellanic System (MS) is located at a distance of about 57 kpc (Cioni et al., 2000)

from the MW and is formed by the LMC, the SMC, the Bridge connecting them and the

Magellanic Stream, a trailing HI component. The LMC is a dwarf irregular galaxy, also

considered as a late type spiral system. The SMC is a dwarf irregular galaxy sometimes

referred to as a dwarf Spheroidal galaxy (dSph; Zaritsky 2000). The LMC has an inclination

angle of ∼ 35 deg (Nikolaev et al. 2004, Olsen & Salyk 2002, van der Marel & Cioni 2001),

but main structures of the galaxy lie reasonably close to the plane of the sky, while the SMC

forms an extended structure almost along the line of sight (Cardwell & Coulson, 1986).

Optical and infrared surveys of the MS show that the LMC and SMC are distinct objects

separated in space by a projected distance of ∼ 20 kpc. However, the HI distribution shows

a different picture.The MCs are connected by a low-metallicity bridge of gas and share a

common gaseous envelope (Putman et al. 2003, Brüns et al. 2005). The existence of such

features suggests that the LMC and the SMC are a binary interacting pair.

The Magellanic Stream is formed by HI gas and does not contain stars (Guhathakurta &

Reitzel, 1998). It trails behind the Clouds at least 150 deg across the sky (Braun & Thilker

2004, Nidever et al. 2010). The Stream has historically been explained as the product of

a tidal or hydrodynamical interaction between the MCs and the MW (Gardiner & Noguchi

1996, Mastropietro et al. 2005, Connors, Kawata & Gibson 2006). This picture is based

on the assumption that the MCs have experienced multiple close passages near the MW.

However, HST proper motion measurements of the MCs (Kallivayalil et al. 2006a; Kalli-

vayalil et al. 2006b) have challenged this model. These studies suggest instead that the

MCs have, at best, completed one obit around the MW, or that they may even be still on

29

2.2. STRUCTURE OF THE LMC

their first passage. Besla et al. (2010) introduced a model to explain the observed large-scale

gas morphology of the MS, according to which the Magellanic Bridge and Stream could be

explained through tidal interaction between the LMC and the SMC. Since the MW is not re-

sponsible for removing material from the system, this picture is consistent with the scenario

of the first infall of the MS towards the MW. There is evidence that the tidal interactions of

the MCs could also account for the internal structure of the LMC (Besla et al., 2012).

2.2 Structure of the LMC

The LMC has a diameter ∼ 4.3 kpc and contains one spiral arm and a bar. The LMC bar is

a long-standing puzzle because it is off-centered relatively to the dynamical centre. Using

relative distance measurements to Cepheids in the LMC, Nikolaev et al. (2004) showed that

the bar is located ∼ 0.5 pc in front of the main disc. There are also evidences that the bar

could be warped relatively to the disc plane, so the east and west ends are nearer the MW

than the middle part (Subramaniam 2003, Lah et al. 2005, Koerwer 2009). The bar is not

seen in the gas distribution (Kim et al., 1998) or as a site of ongoing star formation. Besla

et al. (2012) showed that the internal structure and kinematics of the LMC strongly favour a

scenario in which the MCs have recently (100-300 Myr ago) experienced a direct collision.

The LMC contains large (∼ 1 kpc in diameter) star-forming regions: 30 Doradus, located

slightly above the bar, and Constellation III, located close to the LMC spiral arm (Dolphin

& Hunter, 1998).

The structure of the LMC as traced by probes of different stellar populations was dis-

cussed in Moretti et al. (2014). In this paper we have compared the distribution of RR

Lyrae stars, "hot" eclipsing binary stars (HEBs) and CCs from the OGLE III, OGLE IV and

EROS-2 surveys (Figure 2.1). RR Lyrae stars (age ∼ 10 Gyr) have a larger density in the

central region of the LMC, but in general they are distributed smoothly and likely trace the

halo of the galaxy. On the contrary, CCs and HEBs are strongly concentrated towards the

LMC bar and spiral arm, and almost disappear in the peripheral areas. Fig. 2.1 shows that

distributions of CCs and HEBs are very similar, but HEBs (age∼ 12 Myr) are more sharply

concentrated toward recent star-forming regions (30 Doradus and Constellation III), while

CCs (age ∼ 50− 200 Myr) mostly follow the bar and spiral arm of the LMC. Since HEBs,

RR Lyrae stars and CCs trace different stellar populations, they serve as perfect tools to

study the internal structure of this galaxy.

30

CHAPTER 2. THE LARGE MAGELLANIC CLOUD

Figure 2.1 Distribution of RR Lyrae stars (upper-left), CCs (upper-right) and HEBs (cen-tral) in the LMC. Black points represent sources with OGLE data; red points are EROS-2variables that do not have an OGLE counterpart within 5′′. α0 = 81◦.0 and δ0 = 69◦.0.The sky coverage of the VMC survey (blue rectangles), OGLE III (red contour), OGLE IV(cyan contour) is shown. Green rectangles underline VMC tiles completely observed as ofJuly 2013. Figure is from Moretti et al. (2014).

31

2.3. DISTANCE TO THE LMC

2.3 Distance to the LMC

The LMC is the closest large satellite of the MW and the first step of the cosmic distance

ladder. The galaxy contains a large number of different distance indicators that allows its

distance to be determined through many independent techniques. However, in spite of the

large number of independent measurements of the last twenty years, a general consensus

on the LMC distance has not been reached yet. Furthermore, when pushing distance un-

certainties down to a few percent the effects of sample size, spatial distribution, depth and

geometry become important and properly accounting for the LMC internal structure be-

comes necessary.

Figure 2.2 from Benedict et al. (2002) shows an impressive summary of the different

values for the distance modulus of the LMC published during the ten years from 1992 to

2001. Values from 18.1 to 18.8 mag were reported in literature, with those less than 18.5

mag supporting the so-called “short” distance scale, and those larger than 18.5 mag, the

“long” one. During the last decades dramatic progress in the calibration of the different

distance indicators led the dispersion in the LMC distance modulus to shrink significantly,

thus extreme values such as those listed in Benedict et al. (2002) are not very often seen in

the recent literature (Clementini, 2009).

A number of analyses of the distances to the LMC as derived from different distance

indicators have been performed (Gibson 2000; Benedict et al. 2002; Clementini et al. 2003;

Schaefer 2008; De Grijs et al. 2014). Clementini et al. (2003) compared the LMC distances

obtained from Population I and Population II indicators and showed that all distance deter-

minations converge within 1σ error on a distance modulus (m − M)0 = 18.515 ± 0.085

mag. De Grijs et al. (2014) compiled 233 separate distance determinations, published from

1990 March to 2013 December, and concluded that the canonical modulus of (m−M)0 =

18.49 ± 0.09 mag may be used for all practical purposes. These results are consistent with

the recent determination of direct distances to eight long-period, late-type EBs in the LMC,

which is claimed to be accurate to ∼ 2% (Pietrzynski et al., 2013). These authors found

the distance to the LMC to be: DLMC = 49.97 ± 0.19(stat) ± 1.11(syst) kpc, which

corresponds to the distance modulus (m − M)0 = 18.494 ± 0.049 mag. However, this

result was called into question by Schaefer (2013) who, in addition to concerns on possible

bandwagon effects, also pointed out that Pietrzynski et al. (2013) distance for the LMC dif-

fers significantly from the average distance to four hot, early-type EBs, D=47.1±1.4 kpc,

32


published by Guinan et al. (1998), Fitzpatrick et al. (2002, 2003), and Ribas et al. (2002).

Despite the large number of studies claiming to have determined independently the distance

to the LMC, systematic uncertainties remain. Moreover, there were significant concerns

about a possible “publication bias" affecting distances (Schaefer 2008, Rubele et al. 2012,

Walker 2012). In particular, Schaefer (2008) noted that from 2002 to 2007, 31 independent

papers reported new measurements of the distance of the LMC, and the new values clus-

tered tightly around the value (m−M)0 = 18.5±0.1 mag, adopted by the HST Key Project

on the extragalactic distance scale (Freedman et al. 2001). Schaefer (2008) considered the

effects of "publication bias" to be the most likely cause of the clustering of LMC distance

measurements. Improvements in the instrumentation over the past decade and a half have

allowed the Cepheid distance scale to be extended well beyond the Local Group. Measure-

ments with the HST FGS have provided a direct calibration via parallaxes of 10 Galactic

CCs (Benedict et al., 2007). HST parallaxes of five RR Lyrae stars in the MW were ob-

tained by Benedict et al. (2011). Gaia, the ESA cornerstone mission, successfully launched

on December 2013, will measure parallaxes of one billion stars with unprecedented accu-

racy. All these facts will likely reduce the importance of the LMC as the first rung of the

cosmic distance ladder. But the history shows that the systematic errors are inevitable. The

famous phrase: ”The Hubble Constant at any given time has always been known to 10 per-

cent, despite having changed over the period by a factor of 10" should not be forgotten. For

this reason the careful determination of the distance to the LMC is still crucially important,

since this galaxy provides a sanity check of the validity of the lower rungs of the distance

ladder (Walker, 2012).

This thesis work is focused on three types of distance indicators: CCs, HEBs and RR

Lyrae stars. There are several reasons of this choice. Firstly, how it was discussed in

Section 2.2, HEBs, CCs and RR Lyrae stars probe different stellar populations, hence, serve

as perfect tools to study the internal structure of the LMC. Secondly, these three types of

distance indicators follow relations which zero-points can be calibrated with fundamental

geometric methods. These calibrations will be greatly improved when Gaia parallaxes will

become available.

33

2.3. DISTANCE TO THE LMC

Baade-Wesselink Double-mode

Eclipsing binaries Globular Cluster Dyn. mods

High Amplitude d Scuti Long Period Variables

M Stars Luminosity Main Sequence fitting

Masers Mean V magnitude

Modelling Li-rich Ca stars Nonlinear Pulsation modelling Planetary Nebulae Luminosity

Red Clump Red Clump & RR Lyraes

SN 1987A Statistical parallaxes

Subdwarf fitting Tip of the Red Giant Branch

Trigonometric parallax White Dwarf cooling sequence

19.0018.7518.5018.2518.00 LMC Distance Modulus

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

3637

38

394041

42

43

44

45

46

47

47

48

4950

51

52

53

54

55

56

57

58

5960

61

62

63

64

65

66

67

6869

70

71

71

72

73

74

75

76

77

77

78

7980

8182

83

84

Figure 2.2 Determinations of the distance modulus of the LMC compiled by Benedict etal. (2002). Colors represent the various methods, numbers refer to individual investigations(see Table 10 in Benedict et al. 2002). The thick vertical line denotes the distance modulusadopted by the HST Distance Scale Key Project (Freedman et al., 2001) and the Type IaSupernovae Calibration Team (Saha et al., 1999). Results for the distance modulus of theLMC from Benedict et al. (2002) are in bold.

34


2.4 LMC Surveys

In this thesis work we extensively use the near-infrared photometry being collected by the

VMC survey (Cioni et al., 2011) and visual photometry obtained by the EROS-2, OGLE III

and OGLE IV surveys.

2.4.1 EROS-2

EROS-2 (Expérience pour la Recherche d’Objets Sombres) is a microlensing survey (Tis-

serand et al., 2007) which monitored about 88 deg2 of the LMC discovering a large number

of CCs, RR Lyrae stars, binaries and LPVs, both in the centre and in the outer regions of the

galaxy. The survey was carried out with the Marly 1-m telescope at ESO, La Silla, from July

1996 to February 2003. Observations were performed in two wide passbands, the so-called

REROS band centered close to the I standard band, and the BEROS band intermediate be-

tween the standard V and R bands. The BEROS passband covers the wavelength interval

from 420 to 720 nm, the REROS passband covers the interval from 620 to 920 nm. EROS

magnitudes can be transformed to the Johnson-Cousins standard system to a precision of

∼0.1 mag, using the following equations from Tisserand et al. (2007):

REROS = IC (2.1)

BEROS = VJ − 0.4(VJ − IC) (2.2)

The detection of variable stars and the determination of periods (PEROS) were per-

formed by an automatic pipeline based on the Analysis of Variance (AoV) method and soft-

ware developed by Beaulieu et al. (1997) and Schwarzenberg-Czerny (2003) (see Marquette

et al. 2009 and references therein for further details). The left panel of Figure 2.3 shows the

(BEROS , BEROS−REROS) CMD obtained from the EROS-2 catalogue of the LMC candi-

date variables (red points). The candidate RR Lyrae stars were extracted by selecting in the

CMD objects with 18.46 < BEROS < 20.03 mag, and 0.05 < BEROS − REROS < 0.58

mag (blue points).

Candidates CCs were visually selected in the BEROS versus PEROS diagram on the ba-

sis of the PL relation of CCs. The right panel of Fig. 2.3 shows how the selection was per-

formed. The selected candidate CCs have EROS-2 periods in the range 0.89 < PEROS <

15.85 days, and BEROS magnitudes in the range 13.39 < ⟨BEROS⟩ < 17.82 mag. The

faint magnitude/short period limit allows to reduce the contamination of the candidate CCs

35

2.4. LMC SURVEYS

Figure 2.3 Left panel: BEROS versus BEROS-REROS CMD of LMC candidate variablesfrom the EROS-2 data (red points). A blue box marks the region populated by the RR Lyraecandidates. Right panel: distribution of the EROS-2 candidate variables in the LMC (redpoints) in the LogP versus BEROS plane. Blue points represent the candidate CCs. Figureis from Moretti et al. (2014).

by shorter period variables, such as the RR Lyrae stars, whereas the bright magnitude/long

period limit reflects the bright cut of the EROS-2 data available to us.

As part of the collaboration between the VMC and EROS-2 teams, REROS and BEROS

time-series photometry (and related errors), periods and mean magnitudes for 5800 can-

didate CCs and 16337 candidate RR Lyrae stars were kindly made available to us by the

EROS-2 team. We used these data in oder to study the CCs (see Chapter 3) and the RR

Lyrae stars (see Chapter 6) in the outer regions of the LMC. Moreover, visual inspection

of the light curves of candidate CCs showed that the sample contains also a large fraction

(1768) of EBs. These accidentally found EBs also became subject of this thesis research

(see Chapter 4).

2.4.2 OGLE

The Optical Gravitational Lensing Experiment (OGLE) is a wide-field sky survey started

in 1992. The main goal of this survey was to search for microlensing events (Soszynski et

al. 2008, and references therein). The observing strategy of the project, originally proposed

by Paczynski (1986), was the regular monitoring of brightness of about 200 million stars in

the MCs and Galactic bulge, on time-scales of at least two years, in order to detect lensing

36


events connected with “dark halo” objects. As a byproduct, these observations provided

an enormous database of photometric measurements. OGLE photometry is in the standard

BJohnson, VJohnson and ICousins filters.

The first phase of the project (OGLE I) started in 1992 and lasted till 1995. The 1 m

Swope telescope at the Las Campanas Observatory, Chile, was used (Udalski et al., 1992).

The project was very successful (Udalski et al., 1993) but it suffered from limited availabil-

ity of telescope time. Therefore observations were performed only in the Galactic bulge, and

the covered area on the sky was relatively small. The second phase of the project (OGLE II)

was conducted between 1997 and 2000. The observations were performed with the new

1.3 m Warsaw Telescope dedicated to massive photometric surveys of dense stellar fields

(Udalski et al., 1997). As a byproduct, catalogues of thousands of Cepheids, RR Lyrae stars,

EBs and LPVs in the Galactic Bulge and the MCs were produced (Szymanski, 2005).

The OGLE III phase started on June 2001 with the 1.3 m Warsaw telescope equipped

with the new eight 2048 × 4096 CCD detector mosaic camera at the Las Campanas Ob-

servatory, Chile (Udalski, 2003). OGLE III catalogues are publicly available at the OGLE

website1 and contain 3361 CCs (Soszynski et al., 2008), 24906 RR Lyrae stars (Soszynski

et al., 2009), 26121 EBs (Graczyk et al., 2011) in the LMC and 4630 CCs (Soszynski et

al., 2010a), 2475 RR Lyrae stars (Soszynski et al., 2010b) and 6138 EBs (Pawlak et al.,

2013) in the SMC. For each object, the catalogues provide right ascension, declination,

mean Johnson-Cousins V , I magnitudes, period, I-band amplitude, along with the Fourier

parameters R21, φ21, R31 and φ31 of the I-band light curves (Soszynski et al., 2009).

The most extended area coverage of the MS with OGLE was obtained during the third

phase, however, a significant extension of the observed area is expected with OGLE IV.

Nowadays, only a small region containing the LMC South Ecliptic Pole (SEP) field, ob-

served with the OGLE IV, is publicly available. The so-called Gaia SEP (GSEP) is an area

of about 5.3 deg2 around the SEP, of which a central rhombus-shaped portion of 5 × 0.7

deg2 corresponds to the region that Gaia observed repeatedly during commissioning. The

OGLE collaboration made the GSEP field data available after only two years of observations

because this data could be potentially useful for the Gaia mission. The data set consists of

photometry in the V and I bands for 6789 variables, with a number of data points between

338 and 351 in the I band, and about 29 epochs in the V band. The catalogue of variables

in the GSEP field contains 132 CCs, 686 RR Lyrae stars, 2819 LPVs, 1377 EBs and 156

1http://ogle.astrouw.edu.pl/

37

2.4. LMC SURVEYS

Figure 2.4 Sky coverage of the LMC for EROS-2 (black), OGLE III (red) and the firstrelease of OGLE IV (cyan). VMC tiles are indicated in blue. Tiles already completed as ofJuly 2013 are labelled. α0 = 81◦.0 and δ0 = 69◦.0. Figure is from Moretti et al. (2014).

ellipsoidal variables.

The areas covered in the LMC by the EROS-2 (black), the OGLE III (red) and the

first release of OGLE IV (cyan) surveys are shown in Figure 2.4. EROS-2 provided so far

the largest coverage of the LMC, however, the EROS-2 team made available to us only

catalogues of “candidate" CCs and RR Lyrae stars. Therefore, visual inspection of the light

curves was necessary to validate the classification. Moreover, the EROS-2 observations are

performed in non standard passbands. Therefore, in our study we used the OGLE III data

whenever available (i.e. in the internal regions of the LMC), and the EROS-2 data in the

outer regions of the galaxy.

2.4.3 VMC

The VISTA for Magellanic Clouds near-infrared survey (Cioni et al., 2011) started in Novem-

ber 2009 and is expected to extend beyond the originally planed ∼ 5 years time span. The

main purpose of this survey is to study of the star formation history (SFH) and the 3D struc-

ture of the MS using both constant and variable stars. The strategy, main goals and first data

were presented in Cioni et al. (2011), first results for pulsating variables, based on the VMC

38


Ks-band light curves, were described in Ripepi et al. (2012) for CCs in the LMC, Ripepi

et al. (2014a) for LMC Anomalous Cepheids (ACs), and Ripepi et al. (2014b, accepted to

MNRAS) for Type II Cepheids in the LMC. In Moretti et al. (2014) we present the strategy

of using CCs, RR Lyrae stars and EBs observed by VMC to study the LMC’s structure.

Muraveva et al. (2014a) used the VMC data to study the PL relations of the LMC EBs.

The VMC survey is observing ∼ 200 deg2 of the MS in the Y , J , Ks (λ = 1.02, 1.25 and

2.15 µm, respectively) passbands reaching a sensitivity limit on the stacked images close to

Vega magnitudes Y = 21.1 mag, J = 21.3 and Ks = 20.7 mag with a signal-to-noise ratio

S/N = 10. The survey covers the LMC area (116 deg2) with 68 tiles, the SMC (45 deg2)

with 27 tiles and the Bridge area (20 deg2) with 13 tiles. Two additional tiles cover 3 deg2

in the Stream. The VMC Ks-band are taken over 12 separate epochs (Cioni et al., 2011),

each epoch reaches a limiting magnitude of Ks ∼ 19.3 mag with a S/N ∼ 5. This limit

allows us to detect the minimum light of RR Lyrae stars in both the LMC and SMC. For

bright stars, the VMC survey is limited by saturation at Ks ∼ 11.4 mag. The VMC images

are processed by the Cambridge Astronomical Survey Unit (CASU) through the VISTA

Data Flow System (VDFS) pipeline. The reduced data are then sent to the Wide Field

Astronomy Unit (WFAU) in Edinburgh where the single epochs are stacked and catalogued

by the VISTA Science Archive (VSA; Lewis et al. 2010, Cross et al. 2012).

The VMC coverage of the LMC is shown in Fig. 2.4 (blue) from Moretti et al. (2014).

Tiles which were completely observed (12 epochs) as of July 2013, are labelled. One ad-

ditional LMC tile (tile 6_8) was completed after July 2013. The data for five LMC tiles

(namely tiles 8_8, 8_3, 6_6, 6_4 and 5_5) are now publicly available.

The time sampling of the VMC survey along with the significantly reduced amplitude

of the light variation in the Ks band allows us to derive mean Ks magnitudes with a great

precision (Ripepi et al. 2012, Ripepi et al. 2014a) but we have to rely in our research on

variable star catalogues from the optical microlensing surveys for the identification, coordi-

nates and pulsation properties, such as the period, epoch of maximum light and parameters

of the Fourier decomposition of the visual light curves (Moretti et al., 2014).

39

Chapter 3

Classical Cepheids in the VMC tileLMC 8_3

There are 11 tiles in the LMC that the VMC survey (Cioni et al., 2011) has completely

observed (12 epochs in the Ks band) as of October 2014. In this thesis we have analysed

the CCs in tile LMC 8_3, the RR Lyrae stars in tiles LMC 8_3 and 5_5, and the HEBs in all

LMC tiles, for which Ks data were available as of January 2014.

In this chapter we present results from the analysis of the EROS-2 candidate CCs lo-

cated in the LMC outer tile 8_3. The analysis of this tile was particularly useful to develop

the methods for the classification of candidate CCs from the EROS-2 catalogue. The lower

portion of tile LMC 8_3 is covered also by the OGLE III survey (Fig. 2.4), making it pos-

sible a direct comparison between the EROS-2 and OGLE III results. Periods, epochs of

maximum light, etc. derived in our analysis will be combined with the near-infrared data

from the VMC survey to determine the distance to tile LMC 8_3 from CCs.

3.1 EROS-2 data for candidate Classical Cepheids

The EROS-2 team provided us the catalogue and individual light curves in the BEROS

and the REROS passbands for 5800 candidate CCs in the LMC. Among them we selected

objects which are located in tile LMC 8_3. The coordinates of the center of the tile are: RA

= 05h : 04m : 53.952s , DEC= −66◦ : 15′: 29.880

′′(Cioni et al., 2011), the rotator angle

is -97.2489 deg. In order to extract objects located in this tile from the EROS-2 catalogue

and study the completeness of the EROS-2 catalogue with respect to the VMC catalogue

we performed the following steps:

41

3.1. EROS-2 DATA FOR CANDIDATE CLASSICAL CEPHEIDS

• We selected on the VISTA Science Archive website1 all sources located in tile LMC

8_3 (1024384 objects). This procedure set the range of coordinates (RA and DEC) to

use for extracting objects covering exactly the same area of the EROS-2 catalogue.

• We converted the RA and DEC coordinates of these objects to Cartesian (X and Y)

coordinates using the center of the tile as a reference.

• We calculated new X1 and Y1 coordinates by rotating the reference system such as:

X1 = Xcos(90 − α)− Y sin(90− α) (3.1)

Y 1 = Xsin(90− α) + Y cos(90 − α) (3.2)

where α is the rotator angle

• By plotting the new X1 and Y1 coordinates we derived a straight-looking tile in which

we were able to determine the range covered in each coordinate.

• We applied the same procedure to the EROS-2 catalogue. We converted the RA and

DEC coordinates of the candidate CCs from the EROS-2 catalogue to the Cartesian

(X and Y) coordinates using the center of tile LMC 8_3 as a reference. Then we

determined new X1 and Y1 coordinates of the objects by rotating the reference system

(equation 3.1, 3.2). When both catalogues were in the same system we were able to

extract objects from the EROS-2 catalogue which are located in the area of the VMC

tile LMC 8_3 by using the range of coordinates determined as described above.

By applying the described procedure we extracted 201 candidate CCs located in tile

LMC 8_3, 200 of them have counterparts in the VMC catalogue within a pairing radius of

1 arcsec. The counterpart of one object (EROS-2 id: lm0310k4094) was found within a

pairing radius of 1.2 arcsec. The comparison of the Ks and EROS-2 optical light curves

confirms the star counteridentification.

We analysed the EROS-2 light curves of the 201 candidate CCs with the GRaphical

Analyser of TIme Series (GRATIS) software developed at the Bologna Observatory by

P. Montegriffo (see, e.g., Clementini et al. 2000), and derived BEROS and REROS mean

magnitudes, amplitudes and epochs of maximum light in the BEROS passband for each

object. The results of our analysis are presented in Table 3.1. We corrected the period for

16 stars, since the EROS-2 catalogue provided aliases of the actual periods.1http://horus.roe.ac.uk/vsa/

42

CHAPTER 3. CLASSICAL CEPHEIDS IN THE VMC TILE LMC 8_3

ERO

S-2

idR

AD

ECPe

riod

⟨BEROS⟩

Amp(B)

Epoc

h(m

ax)

⟨REROS⟩

Amp(R)

Col

our

Type

(deg

)(d

eg)

(day

)(m

ag)

(mag

)B

EROS

(mag

)(m

ag)

(mag

)lm

0444

l123

69a

77.7

0978

-65.

7891

20.

6649

9517

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0.27

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6194

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90.

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28cA

Clm

0435

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-65.

7891

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180.

24cA

Clm

0293

l260

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89-6

6.90

412

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90.

2724

5233

4.56

0816

.71

0.18

0.28

cclm

0301

n220

2877

.124

42-6

6.53

385

0.90

4527

17.1

30.

0824

5230

5.65

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0.08

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7sm

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76.8

1620

-66.

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0.57

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126.

7584

17.2

80.

54-0

.27

bin

lm03

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3623

75.5

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7383

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4224

5147

6.66

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.72

0.41

-0.2

2bi

nlm

0437

m21

444

77.6

8774

-66.

0528

70.

9850

9916

.88

0.26

2450

332.

8638

16.6

10.

190.

27cc

lm03

12l1

1935

77.4

3583

-66.

8343

30.

9878

9616

.55

0.28

2451

100.

6816

14.7

70.

181.

78lp

vlm

0427

n127

8876

.053

93-6

6.15

369

1.02

4246

17.6

80.

2524

5145

4.87

2217

.80

0.22

-0.1

3bi

nlm

0300

l857

875

.763

46-6

6.45

715

1.02

7220

16.1

30.

0324

5255

1.69

6014

.97

0.02

1.16

lpv

lm04

24n1

4561

74.9

1334

-65.

8054

51.

0472

3516

.51

0.34

2450

342.

8891

16.7

90.

34-0

.28

bin

lm04

26n2

3242

75.0

2346

-66.

2171

81.

0473

6516

.42

0.36

2451

482.

6228

16.7

50.

34-0

.33

bin

lm03

03n1

5295

77.0

3270

-66.

8369

51.

0695

0317

.39

0.08

2451

060.

8754

17.7

10.

07-0

.31

sm.a

mlm

0427

k197

6675

.278

64-6

6.05

269

1.07

5378

16.6

80.

4724

5118

2.68

7216

.40

0.34

0.28

cclm

0310

k455

077

.559

31-6

6.27

774

1.08

5795

16.6

80.

3324

5188

9.62

7116

.43

0.24

0.25

cclm

0301

m26

336

76.8

7621

-66.

4116

51.

0907

8217

.63

0.12

2452

239.

5837

17.7

80.

15-0

.15

bin

lm04

25n2

6027

75.7

4082

-65.

8787

41.

0908

4917

.78

0.44

2451

510.

5912

17.9

20.

44-0

.15

bin

lm04

37k1

6072

77.2

4041

-66.

0147

11.

1042

4515

.95

0.07

2451

830.

7454

16.2

00.

08-0

.24

sm.a

mlm

0293

k197

8874

.662

97-6

6.71

494

1.11

7755

16.0

90.

0324

5171

6.92

6016

.32

0.03

-0.2

4sm

.am

lm03

10k1

5114

77.5

2638

-66.

3516

41.

1329

1817

.56

0.50

2451

645.

5360

17.7

60.

50-0

.20

bin

lm03

01m

1369

676

.886

49-6

6.32

851

1.16

0762

16.5

90.

3024

5147

2.65

5916

.30

0.21

0.29

cclm

0426

m23

482a

75.0

7795

-66.

0628

41.

1727

8714

.87

0.11

2450

418.

6526

15.2

20.

10-0

.34

sm.a

mlm

0437

n826

777

.381

03-6

6.11

499

1.17

6646

17.3

90.

2424

5162

3.56

3617

.54

0.23

-0.1

6bi

nlm

0303

l234

2876

.800

88-6

6.88

609

1.18

3669

17.5

00.

7324

5085

5.61

2817

.72

0.69

-0.2

2bi

nlm

0312

k155

2377

.480

35-6

6.73

194

1.18

8117

17.5

50.

2124

5177

2.85

0717

.53

0.18

0.02

bin

lm03

10k4

094

77.3

1567

-66.

2746

21.

2125

1416

.76

0.34

2451

266.

5345

16.4

40.

240.

32cc

lm03

02n1

2595

76.3

2740

-66.

8322

31.

2131

5116

.89

0.21

2452

535.

7713

17.1

80.

15-0

.29

bin

lm03

03n1

0523

77.2

0164

-66.

8071

21.

2463

2117

.54

0.44

2451

502.

6255

17.8

80.

44-0

.34

bin

43

3.1. EROS-2 DATA FOR CANDIDATE CLASSICAL CEPHEIDSlm

0302

l135

0475

.711

78-6

6.84

312

1.26

1500

16.4

30.

3524

5122

4.60

8016

.16

0.25

0.27

cclm

0436

k895

276

.366

02-6

5.96

754

1.27

5596

17.7

00.

1724

5078

4.83

0817

.83

0.14

-0.1

4bi

nlm

0437

n926

777

.580

30-6

6.12

241

1.28

0097

16.4

80.

2124

5149

7.71

4216

.15

0.15

0.32

cclm

0293

l140

8974

.996

18-6

6.83

478

1.29

2040

17.4

90.

1124

5031

7.85

9617

.74

0.11

-0.2

6bi

nlm

0291

m59

0575

.361

89-6

6.27

604

1.30

3899

16.3

20.

4024

5125

2.54

2516

.14

0.27

0.18

cclm

0293

n443

875

.103

26-6

6.77

718

1.31

5011

17.5

60.

0924

5115

6.78

8517

.82

0.08

-0.2

6sm

.am

lm04

26m

6757

75.1

0942

-65.

9426

61.

3727

8516

.36

0.14

2451

564.

5990

16.6

00.

12-0

.24

bin

lm04

27k7

569

75.4

8319

-65.

9596

11.

4235

2616

.32

0.58

2452

008.

5146

16.5

90.

54-0

.27

bin

lm04

36m

2067

5a76

.555

30-6

6.06

799

122.

4455

0016

.31

0.51

2450

226.

7490

14.1

30.

282.

18lp

vlm

0300

k223

3175

.895

90-6

6.40

058

1.48

1380

17.6

60.

3424

5135

3.90

4917

.92

0.36

-0.2

6bi

nlm

0300

k232

3375

.716

98-6

6.40

716

1.52

8732

15.5

90.

2224

5035

1.89

7215

.52

0.18

0.08

cclm

0426

n226

2075

.073

70-6

6.21

255

1.52

9313

16.1

20.

1024

5042

5.78

0816

.44

0.10

-0.3

2bi

nlm

0427

m21

459

75.7

9042

-66.

0647

91.

5465

4716

.67

0.30

2450

372.

7347

17.0

10.

29-0

.33

bin

lm03

01k1

2039

76.7

7238

-66.

3204

61.

5500

5815

.87

0.43

2451

934.

6566

15.6

10.

290.

26cc

lm04

24n1

5978

ab

75.1

8656

-65.

8146

91.

5609

3016

.64

0.27

2451

479.

6292

16.4

10.

210.

23cc

lm04

34m

2103

876

.544

71-6

5.69

327

1.58

5547

16.0

80.

1224

5040

4.78

4516

.33

0.12

-0.2

5bi

nlm

0435

l575

277

.272

69-6

5.73

683

1.59

7033

17.5

80.

5624

5162

3.56

3617

.75

0.54

-0.1

7bi

nlm

0305

k407

276

.493

98-6

6.97

811

1.61

9923

17.1

60.

0524

5114

9.64

0317

.29

0.05

-0.1

3sm

.am

lm04

25n1

5511

75.6

5717

-65.

8027

31.

6233

8417

.47

0.26

2451

627.

5233

17.6

90.

25-0

.23

bin

lm04

24n1

0133

74.9

7782

-65.

7724

61.

6353

9016

.06

0.13

2450

498.

6499

16.3

20.

11-0

.25

bin

lm04

27m

4029

75.9

0082

-65.

9288

21.

6363

0016

.06

0.28

2451

784.

7345

15.7

70.

190.

29cc

lm03

02n2

6730

76.2

3651

-66.

9413

21.

6639

4516

.35

0.26

2451

212.

7016

16.0

40.

190.

31cc

lm02

91l1

1728

74.9

6100

-66.

4698

11.

6706

6216

.88

0.30

2451

895.

7390

16.5

10.

220.

37cc

lm03

03m

1696

377

.037

60-6

6.69

697

1.70

2557

16.0

80.

2024

5260

4.76

2215

.90

0.14

0.18

cclm

0301

m21

301

76.9

4809

-66.

3780

41.

7099

1516

.04

0.18

2451

511.

6292

15.7

10.

120.

33cc

lm03

03k5

608

76.5

2968

-66.

6303

41.

7272

3716

.67

0.63

2451

642.

4916

16.4

10.

450.

26cc

lm02

91k2

0831

74.8

0414

-66.

3784

71.

7396

2716

.13

0.34

2452

245.

6216

15.7

10.

230.

42cc

lm04

36l1

4585

76.4

2263

-66.

1591

71.

7569

7115

.73

0.23

2451

830.

7454

16.1

10.

26-0

.38

bin

lm02

93k1

6840

74.6

4961

-66.

6982

31.

7725

0815

.86

0.36

2451

553.

6111

15.6

10.

240.

26cc

lm03

03k1

3861

76.7

6351

-66.

6787

91.

7728

4517

.01

0.10

2450

351.

8972

17.2

00.

10-0

.19

bin

lm02

91m

2186

975

.078

96-6

6.38

380

1.77

4816

17.2

10.

7024

5230

4.67

1717

.40

0.68

-0.1

9bi

nlm

0303

l196

8076

.454

61-6

6.86

658

1.79

3979

15.7

10.

3624

5122

4.60

8015

.51

0.25

0.19

cclm

0291

n743

6a75

.255

35-6

6.44

051

1.79

4205

16.1

40.

2624

5082

6.62

9315

.77

0.18

0.36

cc

44

CHAPTER 3. CLASSICAL CEPHEIDS IN THE VMC TILE LMC 8_3lm

0300

k545

075

.843

31-6

6.28

245

1.80

1747

15.7

20.

0824

5208

4.89

9116

.05

0.07

-0.3

3bi

nlm

0435

n218

9477

.627

52-6

5.84

829

1.80

1802

15.9

20.

3224

5187

8.63

6615

.65

0.23

0.27

cclm

0434

n101

5276

.507

05-6

5.77

485

1.81

4666

15.7

90.

3724

5260

9.67

8315

.52

0.26

0.27

cclm

0301

m24

570

76.8

5416

-66.

3999

91.

8215

2615

.75

0.37

2451

577.

6660

15.4

30.

260.

32cc

lm03

03n1

7856

76.9

2380

-66.

8528

51.

8277

1016

.23

0.12

2451

257.

5461

16.5

40.

11-0

.31

bin

lm04

24m

1510

475

.125

83-6

5.64

843

1.86

1021

15.8

40.

0724

5183

0.71

4216

.11

0.07

-0.2

7bi

nlm

0310

k155

2777

.598

90-6

6.40

988

1.87

2873

15.7

00.

2624

5042

4.83

3115

.41

0.17

0.29

cclm

0291

l253

4974

.751

74-6

6.55

471

1.87

4248

16.8

60.

1224

5182

6.71

3016

.93

0.12

-0.0

7bi

nlm

0310

l188

4877

.465

63-6

6.53

873

1.89

4299

15.7

80.

3324

5075

5.72

5415

.44

0.23

0.34

cclm

0293

l239

8274

.830

80-6

6.89

299

1.89

8197

15.8

20.

3424

5124

6.59

0015

.56

0.24

0.26

cclm

0312

k163

00a

77.3

7623

-66.

7373

61.

9069

0015

.83

0.34

2451

178.

8033

15.4

60.

250.

37cc

lm04

24n2

4516

75.0

5272

-65.

8827

51.

9153

8615

.39

0.08

2451

497.

6153

15.7

10.

11-0

.33

bin

lm03

01l2

2532

76.4

6532

-66.

5436

61.

9251

0115

.93

0.54

2452

265.

6419

16.1

30.

52-0

.20

bin

lm02

91m

1445

275

.271

95-6

6.33

402

1.92

8768

15.7

50.

2224

5155

5.59

1115

.48

0.15

0.26

cclm

0300

m12

894

76.1

8996

-66.

3303

01.

9441

9115

.68

0.19

2451

830.

7320

15.4

80.

140.

20cc

lm04

37m

1575

2a77

.722

49-6

6.00

990

1.96

6639

15.9

10.

2524

5037

6.74

4515

.60

0.16

0.31

cclm

0446

k151

42a

77.7

2235

-66.

0099

11.

9666

4516

.00

0.25

2451

556.

6964

15.6

20.

170.

38cc

lm03

03n1

3787

76.8

3778

-66.

8297

21.

9667

8015

.86

0.22

2452

129.

8190

15.6

60.

150.

21cc

lm03

02l5

812a

75.8

0726

-66.

7917

61.

9886

6015

.70

0.36

2450

835.

6299

15.4

20.

250.

28cc

lm03

01l2

1365

76.6

3322

-66.

5351

82.

0660

4215

.70

0.40

2452

183.

7002

15.3

70.

280.

33cc

lm03

03l2

2257

a76

.401

39-6

6.88

160

2.07

8516

15.6

20.

3024

5165

5.51

8915

.43

0.21

0.19

cclm

0302

l166

6075

.607

09-6

6.86

448

2.08

5372

15.6

90.

2424

5100

6.94

4215

.53

0.17

0.16

cclm

0293

k296

175

.031

27-6

6.61

400

2.09

5923

15.5

60.

3724

5188

9.59

4015

.32

0.26

0.24

cclm

0435

l259

6077

.217

29-6

5.87

469

2.19

0691

15.4

20.

0824

5038

9.80

4415

.70

0.07

-0.2

8sm

.am

lm03

00m

2557

176

.144

99-6

6.41

666

2.20

0747

15.6

10.

2024

5225

7.60

6515

.92

0.20

-0.3

1bi

nlm

0310

k108

1377

.436

35-6

6.42

755

2.21

1064

15.7

50.

2724

5087

9.56

9515

.37

0.19

0.37

cclm

0303

n124

0376

.834

86-6

6.82

148

2.23

4478

16.4

20.

3424

5155

1.64

1016

.69

0.35

-0.2

7bi

nlm

0301

n983

276

.878

18-6

6.45

832

2.24

2879

15.9

60.

1124

5116

9.71

4016

.10

0.11

-0.1

4bi

nlm

0300

m17

427

76.2

0188

-66.

3609

42.

2803

8415

.56

0.27

2452

683.

7579

15.3

10.

190.

25cc

lm03

05m

2711

76.8

7207

-66.

9661

42.

3576

0715

.88

0.87

2452

355.

5595

15.6

40.

610.

23cc

lm03

03k1

2257

76.7

9103

-66.

6688

02.

3681

9215

.47

0.32

2450

369.

8289

15.2

80.

220.

19cc

lm03

10k1

9198

77.3

8119

-66.

3809

22.

3822

4616

.07

0.73

2451

790.

8087

15.7

20.

510.

35cc

lm04

27m

1691

576

.034

40-6

6.02

195

2.38

2868

17.0

90.

3324

5144

7.75

0817

.41

0.31

-0.3

2bi

n

45


0437

m92

6877

.337

03-6

5.96

636

2.39

2800

15.0

40.

1124

5133

9.93

7215

.29

0.10

-0.2

5sm

.am

lm04

35k1

0984

76.9

5992

-65.

6247

52.

4676

2416

.05

0.66

2452

304.

7042

15.6

90.

480.

36cc

lm04

27l1

0110

75.2

8292

-66.

1340

22.

4892

5416

.49

0.28

2451

467.

6728

16.7

50.

31-0

.26

bin

lm03

03m

2160

476

.860

80-6

6.72

639

2.50

7010

15.9

50.

1224

5125

7.54

6116

.29

0.13

-0.3

4bi

nlm

0291

k186

1874

.735

26-6

6.36

418

2.51

8067

16.1

90.

7224

5229

7.65

5215

.76

0.51

0.43

cclm

0291

k119

7974

.843

01-6

6.31

999

2.53

1380

15.7

00.

1824

5233

7.55

5415

.28

0.12

0.42

cclm

0434

l156

0576

.106

65-6

5.82

192

2.54

6594

15.5

10.

2824

5162

7.53

7415

.19

0.19

0.32

cclm

0312

k971

577

.363

94-6

6.66

809

2.56

5057

15.4

90.

3324

5078

8.84

9015

.08

0.24

0.41

cclm

0427

m16

528

75.7

7647

-66.

0217

82.

6082

2616

.01

0.26

2451

793.

7228

16.3

10.

26-0

.30

bin

lm04

25n8

591

75.9

3291

-65.

7526

62.

6152

9915

.95

0.67

2450

435.

7555

15.6

70.

480.

28cc

lm03

03n1

6128

76.8

2415

-66.

8436

42.

6211

9616

.76

0.50

2450

845.

7351

17.0

20.

49-0

.26

bin

lm03

00m

2600

976

.262

00-6

6.41

913

2.68

2304

15.8

70.

9524

5224

2.56

5115

.63

0.67

0.24

cclm

0301

k120

7876

.607

72-6

6.32

178

2.68

4560

15.6

80.

4224

5107

8.76

3115

.39

0.29

0.29

cclm

0305

m11

940

77.0

0428

-67.

0213

62.

6948

1915

.82

0.93

2451

948.

6978

15.5

90.

670.

23cc

lm04

35l7

382

76.9

1829

-65.

7501

42.

6972

9315

.81

0.97

2451

124.

7468

15.4

90.

690.

32cc

lm04

34k9

723

76.2

6202

-65.

6199

52.

7012

9715

.95

0.72

2450

410.

8229

15.5

90.

530.

37cc

lm02

91l5

438

74.8

6958

-66.

4304

72.

7036

8015

.75

0.60

2450

781.

6213

15.8

30.

60-0

.07

bin

lm03

10k1

7708

77.4

5565

-66.

3704

22.

7368

8316

.10

0.68

2451

201.

6079

15.7

00.

490.

40cc

lm04

27l9

939

75.4

6303

-66.

1315

42.

7714

8916

.20

0.57

2451

897.

7396

15.8

80.

460.

32cc

lm04

27k1

5685

75.5

2656

-66.

0762

92.

7915

9515

.55

0.11

2451

398.

8270

15.8

70.

12-0

.32

bin

lm03

10l1

9242

77.4

7706

-66.

5420

72.

8100

2416

.05

0.64

2451

886.

6343

15.6

50.

460.

41cc

lm03

05k7

040

76.5

2476

-66.

9954

22.

8617

4015

.98

0.51

2451

571.

6250

15.5

90.

370.

39cc

lm04

24n2

3353

75.0

9632

-65.

8668

92.

8693

1214

.65

0.28

2450

396.

7221

15.0

40.

32-0

.38

bin

lm03

03l6

182

76.4

9645

-66.

7874

02.

8947

1315

.73

0.89

2450

419.

5964

15.4

90.

590.

24cc

lm04

27n7

395

75.9

9907

-66.

1070

62.

8991

4615

.94

0.66

2451

606.

5799

15.6

20.

460.

32cc

lm03

00k8

884

75.7

5457

-66.

3069

62.

9218

3416

.61

0.31

2450

812.

8682

16.8

90.

26-0

.28

bin

lm04

26n1

7949

75.1

0564

-66.

1767

92.

9246

2816

.23

0.11

2451

872.

6350

16.5

40.

11-0

.31

bin

lm03

03m

5318

76.9

2088

-66.

6270

42.

9260

8216

.82

0.31

2451

920.

6912

17.1

00.

29-0

.27

bin

lm03

03k2

0577

76.6

5658

-66.

7190

82.

9313

1215

.93

0.61

2451

082.

8328

15.6

20.

440.

30cc

lm04

35n9

522

77.6

7406

-65.

7609

12.

9339

4415

.85

0.52

2450

410.

8229

15.5

40.

360.

31cc

lm03

03m

5774

76.9

8484

-66.

6292

42.

9576

1615

.71

0.63

2450

776.

7430

15.5

30.

430.

18cc

lm04

37l1

2785

77.2

8106

-66.

1555

52.

9638

8815

.96

0.66

2451

625.

5553

15.5

90.

480.

37cc

lm04

36n1

8193

a76

.755

75-6

6.18

253

3.00

0081

15.8

10.

8124

5032

1.57

7215

.50

0.58

0.32

cc

46


0426

n224

58a

74.9

9331

-66.

2112

43.

0011

7215

.87

0.72

2451

786.

7259

15.5

60.

390.

31cc

lm02

91k2

974

74.8

3436

-66.

3202

63.

0488

6316

.01

0.71

2451

455.

7233

15.4

20.

460.

59cc

lm04

37l7

188

76.9

3822

-66.

1091

53.

0622

7815

.94

0.63

2451

317.

4928

15.5

40.

440.

41cc

lm03

10l9

678

77.4

4955

-66.

5960

73.

0902

7315

.03

0.22

2452

247.

8307

14.6

80.

150.

35cc

lm04

35k1

6509

77.1

8997

-65.

6611

53.

0914

2215

.79

0.54

2451

329.

4786

15.4

60.

410.

33cc

lm03

00m

5551

76.0

1798

-66.

2797

13.

0954

4015

.87

0.60

2451

595.

6926

15.6

00.

430.

26cc

lm03

03k8

191

76.5

7712

-66.

6457

23.

1133

8715

.83

0.69

2451

905.

7471

15.5

60.

490.

27cc

lm03

01l8

214

76.5

8141

-66.

5965

53.

1231

5815

.91

0.66

2450

800.

6827

15.4

70.

470.

43cc

lm02

91m

2221

575

.078

76-6

6.42

292

3.12

7545

15.8

10.

6524

5249

5.81

3715

.43

0.46

0.39

cclm

0436

l797

276

.307

73-6

6.10

797

3.12

8903

15.7

30.

7924

5200

1.55

5215

.36

0.56

0.36

cclm

0436

l209

2476

.071

18-6

6.20

891

3.14

0133

16.1

10.

4524

5268

1.74

4715

.70

0.30

0.41

cclm

0300

k130

8175

.733

68-6

6.33

645

3.14

8857

15.8

70.

3224

5157

7.66

6015

.53

0.23

0.34

cclm

0427

n176

7675

.681

83-6

6.19

575

3.16

7981

15.7

60.

8224

5246

6.88

1715

.45

0.58

0.31

cclm

0301

n160

4976

.805

37-6

6.49

814

3.18

6794

15.2

90.

3124

5107

5.84

6314

.92

0.23

0.37

cclm

0300

l988

375

.660

61-6

6.46

650

3.18

8358

16.0

00.

3324

5111

0.76

0915

.58

0.24

0.42

cclm

0303

k193

4176

.736

29-6

6.71

116

3.19

3448

15.7

00.

7524

5175

6.86

0315

.47

0.54

0.23

cclm

0434

k243

1576

.448

97-6

5.72

779

3.20

7143

15.7

50.

7524

5134

2.93

8015

.38

0.54

0.37

cclm

0444

k211

8877

.724

76-6

5.69

096

3.24

5950

15.9

40.

6224

5158

3.67

5615

.56

0.45

0.38

cclm

0301

n144

2276

.953

64-6

6.48

692

3.26

4528

15.7

00.

7724

5112

5.62

8415

.34

0.54

0.36

cclm

0435

k200

2377

.255

56-6

5.68

476

3.28

1595

16.6

80.

1924

5037

2.76

0716

.90

0.22

-0.2

2bi

nlm

0435

n137

7877

.560

30-6

5.79

180

3.28

6657

15.7

00.

6924

5258

2.62

9915

.39

0.48

0.31

cclm

0436

l190

0776

.280

93-6

6.19

386

3.30

1123

14.9

60.

0524

5224

0.57

5415

.26

0.05

-0.3

0bi

nlm

0437

k165

8676

.911

84-6

6.02

031

3.32

7489

16.0

10.

4824

5190

1.74

7215

.59

0.34

0.42

cclm

0301

k175

1376

.717

01-6

6.35

814

3.32

8361

16.0

10.

5724

5176

3.89

4115

.66

0.42

0.35

cclm

0300

m80

1076

.021

62-6

6.29

691

3.37

7967

15.8

70.

4524

5157

5.66

2815

.55

0.32

0.32

cclm

0301

m60

2576

.831

90-6

6.27

650

3.41

2130

15.7

50.

8024

5149

1.64

3015

.43

0.56

0.32

cclm

0424

m26

545

75.0

6331

-65.

7273

83.

5094

4415

.69

0.83

2451

908.

7288

15.3

50.

590.

34cc

lm03

10l1

8849

77.5

5575

-66.

5834

73.

5187

8515

.75

0.68

2451

067.

7701

15.3

30.

490.

41cc

lm04

35l2

4878

76.9

1970

-65.

8690

03.

5407

3915

.76

0.66

2452

605.

7595

15.3

70.

470.

39cc

lm04

36k1

1123

76.4

2184

-65.

9850

43.

5992

9915

.69

0.61

2451

951.

6654

15.3

50.

430.

34cc

lm04

35l1

1832

77.2

6535

-65.

7781

63.

6301

8615

.85

0.30

2452

096.

8743

15.4

50.

220.

41cc

lm03

03l2

4720

76.7

1642

-66.

8940

63.

6306

6516

.40

0.05

2451

920.

6912

16.6

20.

05-0

.22

sm.a

mlm

0425

n188

7475

.938

26-6

5.82

298

3.64

9476

15.6

50.

8324

5231

5.63

1215

.35

0.59

0.30

cc

47


0303

m26

388b

77.0

9012

-66.

7525

83.

7004

8215

.38

0.31

2451

116.

8084

15.2

30.

230.

15cc

lm03

00k1

5119

75.6

4848

-66.

3508

93.

7058

0015

.73

0.42

2451

153.

6115

15.3

50.

310.

38cc

lm04

27l7

011

75.4

3113

-66.

1062

13.

7350

4415

.53

0.79

2452

259.

5869

15.1

90.

550.

35cc

lm02

91l4

891

75.0

0036

-66.

4261

43.

7518

2915

.15

0.51

2450

838.

6385

15.4

30.

50-0

.27

bin

lm03

03m

3523

76.8

6127

-66.

6162

23.

7564

9415

.62

0.54

2450

879.

5630

15.3

70.

380.

25cc

lm03

02k1

5867

75.6

5471

-66.

7497

53.

8328

0915

.50

0.73

2451

255.

5600

15.1

30.

530.

38cc

lm04

37m

3722

77.5

2490

-65.

9244

33.

8936

8715

.69

0.32

2451

595.

7028

15.3

10.

230.

38cc

lm04

36k1

3349

76.2

3076

-66.

0033

73.

9163

6215

.67

0.61

2451

761.

8185

15.2

70.

440.

40cc

lm04

37l1

4075

77.2

0916

-66.

1657

83.

9650

0015

.70

0.47

2451

306.

5146

15.2

80.

330.

41cc

lm03

03n1

9840

77.1

9733

-66.

8618

83.

9681

6815

.53

0.72

2450

532.

5716

15.3

10.

510.

22cc

lm04

37n1

8565

77.6

8727

-66.

2021

63.

9726

6415

.76

0.66

2450

763.

7960

15.4

20.

470.

35cc

lm03

00m

2201

975

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69-6

6.39

246

3.98

6529

16.3

40.

4424

5146

8.61

7416

.62

0.46

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8bi

nlm

0303

n114

62a

76.8

4417

-66.

8156

74.

0034

1415

.55

0.53

2452

582.

6163

15.2

60.

370.

29cc

lm04

35m

2108

877

.427

68-6

5.68

669

4.05

0212

15.6

00.

4224

5183

3.73

9815

.20

0.31

0.40

cclm

0303

n141

1076

.823

39-6

6.83

168

4.24

0275

15.5

40.

6024

5112

5.62

8415

.26

0.42

0.28

cclm

0436

n217

7576

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75-6

6.21

120

4.32

5470

15.4

50.

3324

5124

6.62

7715

.15

0.28

0.30

cclm

0436

l174

6576

.050

97-6

6.23

806

4.37

7315

14.7

10.

1224

5232

7.61

6915

.00

0.13

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9sm

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lm03

10k1

9077

77.5

7698

-66.

3797

74.

3908

8015

.48

0.47

2450

369.

8365

15.0

60.

340.

41cc

lm03

03n1

9424

77.0

5204

-66.

8607

84.

4607

3315

.46

0.65

2451

844.

7158

15.2

00.

450.

26cc

lm03

00n1

8729

76.0

9649

-66.

5252

74.

4841

9315

.63

0.38

2451

563.

6306

15.2

40.

270.

40cc

lm03

01n2

1884

76.8

2732

-66.

5812

44.

5081

6115

.43

0.66

2450

855.

6128

14.9

90.

470.

44cc

lm03

00k1

4043

75.5

9119

-66.

3434

04.

6050

9915

.49

0.55

2452

207.

5989

15.1

30.

390.

36cc

lm04

36n2

2963

76.5

6901

-66.

2204

04.

6621

9115

.44

0.71

2451

899.

7779

15.0

60.

490.

38cc

lm04

36k1

6816

76.1

8391

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0304

94.

7514

1915

.46

0.25

2450

756.

7592

15.0

30.

180.

42cc

lm04

27l1

2767

75.2

7200

-66.

1554

44.

8059

3215

.88

0.13

2451

815.

7447

16.1

50.

13-0

.27

bin

lm04

25n1

4050

76.0

3249

-65.

7895

14.

8192

0415

.36

0.39

2450

846.

7634

15.0

30.

280.

33cc

lm04

36n2

3124

76.8

2989

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2207

34.

8710

8015

.47

0.67

2451

492.

6289

15.1

00.

480.

37cc

lm04

26n2

3478

75.1

8067

-66.

2184

94.

9366

4416

.27

0.10

2451

751.

9015

16.2

40.

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04sm

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lm04

27k1

3855

75.5

5629

-66.

0060

55.

0164

6915

.64

0.45

2451

948.

6800

15.8

90.

43-0

.25

bin

lm04

27k7

505

75.4

2766

-65.

9593

95.

1229

6415

.17

0.11

2452

355.

5460

15.4

40.

13-0

.27

bin

lm04

27m

1369

775

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42-6

6.07

558

5.60

6188

15.0

80.

5924

5151

0.59

1214

.76

0.41

0.33

cclm

0427

n162

72a

76.0

3168

-66.

1820

56.

0037

4014

.97

0.12

2451

564.

5990

15.2

70.

12-0

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bin

lm03

03k2

3599

76.5

7203

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7373

16.

4630

8515

.36

0.43

2451

038.

8223

15.5

90.

41-0

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bin

48


0427

n121

2275

.865

53-6

6.14

977

7.19

4033

15.4

80.

1824

5212

3.84

1915

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0.20

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9bi

nlm

0435

m12

381

77.5

5651

-65.

6277

47.

6965

5115

.87

0.62

2451

888.

6354

16.0

40.

57-0

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bin

lm04

34k8

023

76.2

3518

-65.

6071

88.

1263

9614

.54

0.70

2451

341.

9322

14.1

10.

510.

43cc

lm04

36k1

1112

76.3

8695

-65.

9850

011

.331

810

14.3

90.

0824

5256

2.67

7214

.11

0.06

0.27

sm.a

mlm

0436

m12

100a

76.7

5148

-65.

9970

610

9.89

9010

16.1

70.

5124

5026

2.48

3614

.29

0.21

1.88

lpv

lm03

04m

5953

75.9

4165

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9901

22.

7122

2116

.03

0.67

2450

800.

6827

15.6

60.

490.

36cc

Tabl

e3.

1:Pr

oper

ties

ofca

ndid

ate

CC

sin

tile

LMC

8_3

(Col

umn

1:ER

OS-

2id

entifi

catio

nnu

mbe

r;C

olum

n2:

Rig

htas

cens

ion

from

the

ERO

S-2

cata

logu

e;C

olum

n3:

Dec

linat

ion

from

the

ERO

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cata

logu

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olum

n4:

Perio

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49

3.2. CLASSIFICATION OF CANDIDATE CLASSICAL CEPHEIDS

EROS-2 id P1,GRATIS P2,GRATIS P2/P1,GRATIS P1,OGLE III P2,OGLE III P2/P1,OGLE III

(day) (day) (day) (day)lm0424n15978 1.560930 1.135416 0 .7274 - - -lm0303m26388 3.700482 2.653466 0.7171 3.700349 2.653591 0.7171

Table 3.2 Double-mode CCs in tile LMC 8_3. (Column 1: EROS-2 identification of thestar; Column 2: First period derived with GRATIS; Column 3: Second period derived withGRATIS; Column 4: Ratio of the periods; Column 5: First period from the OGLE IIIcatalogue; Column 6: Second period from the OGLE III catalogue; Column 7: Ratio of theperiods from OGLE III).

By analysing the light curves with GRATIS we discovered two double-mode pulsators,

namely lm0303m26388 and lm0424n15978. For lm0303m26388 our second periodicity

is also confirmed by the OGLE III survey, while for lm0424n15978 there is no OGLE III

counterpart. Information about these two objects is presented in Table 3.2.

3.2 Classification of candidate Classical Cepheids

The visual inspection of the light curves of the 201 candidate CCs returned a sample of 126

bona-fide CCs, 58 EBs, 13 variables with small amplitudes (generally around 0.1 mag or

lower) and 4 LPVs. The latter accidentally fall in the sample of the candidate CCs, based

on the PEROS and BEROS values, because their EROS periods are aliases of the actual

periods, which are usually in the range from tens to thousands of days for LPVs. In the

sample of confirmed Cepheids we have also found two candidate Anomalous Cepheids:

lm0435n13603 (P=0.664997 days) and lm0444l12369 (P=0.664995 days). These objects

have shorter periods, than CCs, and are relatively fainter being located in the lower part

of the Cepheid’s region on the CMD (1.2-1.4 mag brighter than HB stars). Results of our

classification for the 201 candidate CCs in tile LMC 8_3 are presented in Table 3.1.

OGLE III covers the lower 1/4 of tile LMC 8_3 and identified 52 CCs in this region,

of which 36 are in common with EROS-2 and 16 do not have a counterpart in the EROS-2

catalogue of CC candidates. Four of these 16 objects have a counterpart in the general cat-

alogue of EROS-2 stars but they were not classified as CC candidates. Information about

the 36 CCs in common between the EROS-2 and OGLE III catalogues is presented in Ta-

ble 3.3. There are a total number of 142 CCs in this tile, of which 141 have a counterpart

in the VMC catalogue within a pairing radius of 1′′. This corresponds to a 99 % complete-

ness of the VMC survey with respect to the number of CCs identified by both EROS-2 and

50


0 1 218

17

16

15

14

0 0.5 118

17

16

15

14

Log(P)0 0.5 1

18

17

16

15

14

Log(P)

Figure 3.1 Left panel: BEROS , BEROS − REROS CMD of EROS-2 candidate CCs in the

VMC tile LMC 8_3. Blue crosses, green filled circles and black filled triangles represent

EBs, bona-fide CCs and small amplitude variables, respectively. Red filled squares are

LPVs. Black empty circles are 36 CCs observed also by the OGLE III survey, confirming

their classification as CCs. Right panel: PL relations in the REROS (upper-right) and

BEROS (lower-right) bands of the EROS-2 candidate CCs in tile LMC 8_3. Symbols and

colours coding are as in the left panel. The LPVs were omitted. Figure is from Moretti et

al. (2014).

OGLE III.

The results of the classification show that the candidates CCs selected by the EROS-2

on the basis of the PL distribution (right panel of Fig. 2.3) are mainly contaminated by EBs.

We have investigated whether we could find methods to clean the candidate CCs without

checking visually all the light curves, and found that the EROS-2 CMD is well suited for

this purpose, as also was pointed out by Spano et al. (2011) in their Fig. 8. The left panel of

Fig. 3.1 shows the BEROS , BEROS − REROS CMD of the EROS-2 candidate CCs in tile

LMC 8_3. In the CMD objects classified as EBs (blue crosses) after visual inspection of the

light curves are very well separated and definitely bluer (BEROS−REROS < 0.1 mag) than

sources confirmed to be CCs (green circles). Furthermore, both binaries and CCs appear

to be constrained in small BEROS − REROS colour ranges. A number of small amplitude

51

3.3. STRATEGY FOR EXTRACTING BONA-FIDE CLASSICAL CEPHEIDS

variables (black triangles in Fig. 3.1) also fall in the region of EBs. As suggested by the

amplitude smaller than 0.1 mag, the typical periods and the blue colours, they likely are

main sequence variables such as β Cepheids, Be stars, slowly pulsating B variables (see, e.g

Baldacci et al. (2005) and reference therein, for characteristics of these types of variables).

Four LPVs (red squares in Fig. 3.1) lie at colours redder than BEROS −REROS ∼ 1 mag.

Spano et al. (2011) analysed light curves of 856864 variables in the EROS-2 data obtaining

a final list of 43551 LPVs in the LMC. The catalogue of 5800 EROS-2 candidate CCs has

296 objects in common with the LPV catalogue from Spano et al. (2011). The 4 LPVs

found in tile LMC 8_3 are all included in the catalogue of LPVs published by Spano et al.

(2011).

The right panel of Fig. 3.1 shows the PL relations in the REROS (upper panel) and

BEROS (lower panel) passbands of the EROS-2 candidate CCs (the LPVs were omitted).

The bona-fide CCs are distributed along the two loci occupied by first-overtone and funda-

mental mode CCs, respectively. EBs significantly contaminate the Cepheid’s BEROS PL,

while seem to be more separated from bona-fide CCs in the REROS PL. To summarize,

by combining BEROS , BEROS −REROS CMD and the BEROS , REROS PLs it should be

possible to separate quite easily bona-fide CCs from binaries and small amplitude variables.

3.3 Strategy for extracting bona-fide Classical Cepheids

In the analysis of the VMC tiles for which information on the variable stars is available

only from the EROS-2 survey, we will use the following strategy to extract bona-fide CCs

from the EROS-2 sample of candidate CCs. As a general rule we expect that sources with

0.1 < (BEROS−REROS) < 1 mag are likely to be bona-fide CCs, sources with (BEROS−

REROS) < 0.1 mag are likely to be EBs, and objects with (BEROS−REROS) ≥ 1 mag are

LPVs (Moretti et al., 2014). According to this method out of the 5800 EROS-2 candidate

CCs in the LMC, 3484 (60.1 %) are bona-fide CCs, 2003 (34.5 %) are EBs and 313 (5.4 %)

are likely LPVs. However, we are aware that the above colour separations may sometimes

be too crude. Especially for tiles where reddening is large and patchy (internal regions of

the LMC), there may be sources with colours between the two main distributions that may

belong to one or the other group, and thus will need to be checked visually.

In order to check the robustness of the described procedure and verify that bona-fide

CCs selected on the basis of the colour-cuts in the CMD are no longer contaminated by

52


Figure 3.2 Left panel: CMD of the 3488 candidate CCs that have a counterpart in the

OGLE III catalogue of EBs or CCs. Blue points represent EROS-2 candidate CCs with

colour BEROS − REROS < 0.1 mag. Cyan circles represent EROS-2 candidate CCs with

an OGLE III counterpart classified as EBs. Green points are EROS-2 candidate CCs with

colour 0.1 < (BEROS − REROS) < 1.0 mag. Black circles are EROS-2 candidate CCs

with an OGLE III counterpart classified as CCs. Red crosses mark two CCs, that fall in

the region of the CMD mainly occupied by EBs. Red filled circles are EBs falling in the

region of the CMD occupied by bona-fide CCs (67 objects). Right panel: PL in the REROS

passband of the objects with 0.1 < (BEROS −REROS) < 1.0 mag. Figure is from Moretti

et al. (2014).

53

3.3. STRATEGY FOR EXTRACTING BONA-FIDE CLASSICAL CEPHEIDS

spurious sources, we have compared our selection of the EROS-2 candidate CCs with the

OGLE III catalogues of CCs and EBs. The EROS-2 catalogue of candidate CCs contains

a total number of 5800 sources, this number reduces to 5487 if only objects with colour

bluer than 1.0 mag are selected (i.e after discarding the LPVs). Of these 5487 objects, 3488

have a counterpart in the OGLE III catalogues of CCs and EBs within a pairing radius of 1

arcsec.

The left panel of Figure 3.2 shows the CMD of the 3488 stars with a counterpart in

the OGLE III catalogue. This sample contains 2357 CCs and 1062 EBs according to the

colour-cut criteria and the OGLE III classification. There are only two objects (red crosses

in Fig. 3.2) that we would classify as EBs based on their colours and are instead CCs ac-

cording to the OGLE III classification and the visual inspection of the light curves. These

are stars with EROS-2 identification lm0551n20500 and lm0036k8214, corresponding to

OGLE-LMC-CEP-0962 and OGLE-LMC-CEP-2595, respectively. The latter has a clean

light curve, while OGLE-LMC-CEP-0962 has variable mean luminosity. According to the

OGLE III remarks its classification as CC is uncertain. On the other hand, there are 67 ob-

jects (red filled circles in Fig. 3.2) that we would classify as CCs based on their colours and

are instead EBs both according to OGLE III and the visual inspection of the EROS-2 light

curves. This corresponds to a 3 % contamination of the bona-fide CCs sample. Thirty-three

of these binaries have colour in the range [0.1;0.2] mag, suggesting that stars with these

colours need visual inspection to be properly classified.

The right panel of Fig. 3.2 shows the PL distributions in the REROS passband of the

sources with 0.1 < (BEROS − REROS) < 1.0 mag. There are two separate sequences

formed by the fundamental and the first-overtone mode pulsators. Part of EBs that still

contaminate the CCs sample (red points in Fig. 3.2) deviate significantly from the CCs

sequences and could be eliminated with a sigma-clipping procedure. This will allow us to

further reduce the 3 % contamination of the sample of bona-fide CCs. In summary, the

application of colour-cuts in the CMD is a robust criterion that combined with the analysis

of the scatter in the PL relations allows one to extract a sample of bona-fide CCs more

than 97 % clean from contaminating sources (Moretti et al., 2014). In any case, a 3 %

contamination is not expected to affect significantly the PLKs relations of CCs in regions

where only the EROS-2 data are available.

54


OG

LEII

Iid

ERO

S-2

idR

AD

ECTy

peI

VP

(HH

:MM

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(DD

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LE-L

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116

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6730

5:04

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2516

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MC

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m16

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6216

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1.70

2563

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LE-L

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85:

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4415

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LE-L

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15.9

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GLE

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lm02

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3982

4:59

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MC

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k163

005:

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44:1

4.7

115

.312

15.8

981.

9069

54O

GLE

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C-C

EP-1

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3787

5:07

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41

15.4

6716

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1.96

6774

OG

LE-L

MC

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2lm

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l581

25:

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3.78

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47:3

0.6

115

.242

15.8

271.

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42O

GLE

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C-C

EP-0

911

lm03

03l2

2257

5:05

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39-6

6:52

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01

15.2

10-9

9.99

2.07

8685

OG

LE-L

MC

-CEP

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6lm

0302

l166

605:

02:2

5.73

-66:

51:5

2.4

115

.381

16.0

612.

0854

01O

GLE

-LM

C-C

EP-0

618

lm02

93k2

961

5:00

:07.

52-6

6:36

:50.

71

15.1

2415

.638

2.09

5957

OG

LE-L

MC

-CEP

-101

8lm

0305

m27

115:

07:2

9.33

-66:

57:5

8.3

F15

.525

16.1

282.

3576

19O

GLE

-LM

C-C

EP-0

988

lm03

03k1

2257

5:07

:09.

87-6

6:40

:07.

71

15.0

4115

.595

2.36

8493

OG

LE-L

MC

-CEP

-112

1lm

0312

k971

55:

09:2

7.37

-66:

40:0

5.4

114

.913

15.5

352.

5649

91O

GLE

-LM

C-C

EP-1

039

lm03

05m

1194

05:

08:0

1.06

-67:

01:1

7.1

F15

.448

16.0

962.

6948

34O

GLE

-LM

C-C

EP-0

818

lm03

04m

5953

5:03

:46.

02-6

6:59

:24.

6F

15.4

8916

.182

2.71

2216

OG

LE-L

MC

-CEP

-093

9lm

0305

k704

05:

06:0

5.98

-66:

59:4

3.9

F15

.483

16.2

022.

8617

35O

GLE

-LM

C-C

EP-0

933

lm03

03l6

182

5:05

:59.

19-6

6:47

:15.

0F

15.3

4115

.977

2.89

4750

OG

LE-L

MC

-CEP

-096

0lm

0303

k205

775:

06:3

7.62

-66:

43:0

8.8

F15

.432

16.1

412.

9312

99O

GLE

-LM

C-C

EP-1

035

lm03

03m

5774

5:07

:56.

39-6

6:37

:45.

4F

15.2

7115

.913

2.95

7635

OG

LE-L

MC

-CEP

-113

4lm

0310

l967

85:

09:4

7.91

-66:

35:4

6.1

114

.575

15.1

623.

0900

31O

GLE

-LM

C-C

EP-0

951

lm03

03k8

191

5:06

:18.

53-6

6:38

:44.

7F

15.3

7515

.992

3.11

3395

OG

LE-L

MC

-CEP

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2lm

0301

l821

45:

06:1

9.60

-66:

35:4

7.8

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16.0

753.

1232

34O

GLE

-LM

C-C

EP-0

974

lm03

03k1

9341

5:06

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76-6

6:42

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3.19

3414

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LE-L

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0lm

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l188

495:

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3.39

-66:

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0.7

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16.1

253.

5187

52O

GLE

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EP-1

064

lm03

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85:

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GLE

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EP-1

013

lm03

03m

3523

5:07

:26.

73-6

6:36

:58.

5F

15.1

3615

.890

3.75

6495

55

3.3. STRATEGY FOR EXTRACTING BONA-FIDE CLASSICAL CEPHEIDSO

GLE

-LM

C-C

EP-0

762

lm03

02k1

5867

5:02

:37.

14-6

6:44

:59.

4F

14.9

6115

.632

3.83

2815

OG

LE-L

MC

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-108

5lm

0303

n198

405:

08:4

7.38

-66:

51:4

3.0

F15

.063

15.8

273.

9681

88O

GLE

-LM

C-C

EP-1

003

lm03

03n1

1462

5:07

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63-6

6:48

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15.0

8115

.847

4.00

3405

OG

LE-L

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4lm

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105:

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4.5

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2402

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GLE

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EP-1

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lm03

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5:08

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6:51

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.774

4.46

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LE-L

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56

Chapter 4

Eclipsing binaries in the LMC

The EROS-2 sample of candidate CCs is significantly contaminated by EBs. These objects

have blue colours, hence, we classed them as “hot” eclipsing binaries (HEBs; Muraveva et

al. 2014a). In this chapter we describe the results of our analysis of these HEBs.

4.1 EROS-2 data for eclipsing binaries

As it was described in Section 3.3 a large number of objects with colour (BEROS−REROS) <

0.1 mag are EBs. It was also noted that sources with colour 0.1 < (BEROS−REROS) < 0.2

mag are located in the CMD between the distributions of CCs and EBs and may belong to

one or the other group. Thus, stars with these colour need visual inspection of the light

curves to be properly classified. In order to characterise the EROS-2 EBs that contaminate

the sample of LMC bona-fide CCs we extract from the EROS-2 catalogue of candidate CCs

all objects with colour (BEROS − REROS) < 0.2 mag (2085 sources). We explicitly note

that the EROS-2 catalogue of candidate variables contains a much larger number of EBs.

Recently, Kim et al. (2014) identified new EBs in the LMC based on the full EROS-2 dataset

by applying a machine learning approach. However, in this thesis work we focused only on

the objects contaminating the CC sample.

The analysis of these sources was performed running GRATIS on the REROS light

curves and showed that 83 objects from the sample are bona-fide CCs, 225 are small ampli-

tude variables, nine objects have light curves which are too noisy to be classified, and 1768

stars are EBs. Information on these EBs is presented in Table A.1 (Appendix).

We transformed the BEROS , REROS average magnitudes of the sources to V , I stan-

dard magnitudes by applying equations 2.1 and 2.2 (Subsection 2.4.1). The left panel of

Figure 4.1 shows the distributions of mean V, I magnitudes and V − I colours for our sam-

57

4.1. EROS-2 DATA FOR ECLIPSING BINARIES

17 16 15 140

20406080

17 16 15 140

20406080

17 16 15 140

20406080

100

-1 -0.5 00

100200300400500

5 10 15 20

0

100

200

300

400

Period (days)

Figure 4.1 Distributions of mean V, I magnitudes and V −I colours (left panels), and period(right panel) of the LMC EBs in our sample. Figure is from Muraveva et al. (2014a).

ple of EBs. The mean V and I magnitudes range from ∼17.8 to ∼13.2 mag (which reflects

the initial cuts in magnitude used to extract the sample of candidate CCs from the EROS-2

catalogue) and from ∼18.1 to ∼13 mag, respectively, with a peak around 17.1-17.2 mag in

both bands. The V − I colours range from ∼ −1.3 to 0.33 mag and peak at V − I = −0.3

mag, which reflects instead the colour selection we applied to separate binaries from bona-

fide CCs. According to their blue colours the EBs in our sample are mainly composed by

hot components: main sequence stars or blue giants, hence, we classified them as HEBs.

We have compared the periods provided by the EROS-2 survey for the HEBs with those

determined by the visual inspection of light curves with GRATIS (PGRATIS). For the ma-

jority of binaries PGRATIS is in good agreement with PEROS . However, in some cases,

PEROS was a harmonic or a subharmonic of the actual period. We corrected the period of

225 objects in the sample by multiplying PEROS by different constants until the shape of

the light curve was consistent with that of an EB. The same technique was used by Derekas

et al. (2007) as part of the redetermination of periods for 3031 EBs in the MACHO cata-

logue. Examples of the light curves before and after the period correction are presented in

Figure 4.2. The systems in the middle and bottom panels of Figure 4.2 have rather eccen-

tric orbits which hinders the automatic determination of the period. In some cases it was

not clear if EROS-2 determined aliases of the true period or if the binary star had only one

58

CHAPTER 4. ECLIPSING BINARIES IN THE LMC

Figure 4.2 Light curves of EBs before (left panels) and after (right panels) correction of theperiod (see text for details). Figure is from Muraveva et al. (2014a).

strong expressed minimum. For these objects we decided to use the periods provided by

EROS-2.

We studied the period distribution of our sample of HEBs even though the true periods

of these objects cover a relatively narrow range (from ∼ 0.89 to ∼ 20 day). The distribution

of periods is shown on the right panel of Fig. 4.1. Most of our HEBs are short-period

systems. The distribution sharply peaks between 1 and 2 days and the majority of HEBs in

our sample (94 %) have periods shorter than 5 days.

4.2 Cross-correlation with other catalogues of eclipsing binariesin the LMC

Nine different catalogues of EBs detected in the LMC by the microlensing surveys have

been published. During the first stage of the EROS survey, 79 candidate EBs were identified

in the bar of the LMC (Grison et al., 1995). The MACHO survey identified an initial sample

of 611 LMC EBs (Alcock et al., 1997). Subsequently, Derekas et al. (2007) reanalysed the

eclipsing variables in the MACHO database, corrected their periods and presented a “clean"

sample of 3031 EBs. Faccioli et al. (2007) provided a new sample of 4634 EBs in the LMC

from the MACHO catalogue, expanding the previous sample of 611 objects from Alcock et

59

4.2. CROSS-CORRELATION WITH OTHER CATALOGUES OF ECLIPSINGBINARIES IN THE LMC

al. (1997). Using the OGLE II data, 3332 EBs were identified in the LMC (Wyrzykowski

et al. 2003, Groenewegen 2005, Graczyk & Eyer 2010). Graczyk et al. (2011) provided

a sample of 26121 LMC EBs detected by the OGLE III survey. Finally, Soszynski et al.

(2012) identified 1377 EBs and 156 ellipsoidal variables in the GSEP area based on the

OGLE IV survey.

We cross-correlated our sample of 1768 HEBs with the catalogues of EBs identified in

the LMC by the various microlensing surveys. Specifically, we considered: the first stage

of the EROS survey (Grison et al. 1995), the MACHO survey (Alcock et al. 1997; Derekas

et al. 2007; Faccioli et al. 2007), the OGLE III (Graczyk et al. 2011) and IV (Soszynski

et al. 2012) surveys. Objects in the various catalogues were cross-identified when their

right ascension and declination differed by less than 10′′, and the periods differed by less

than 1%. We also considered objects located within less than 10′′ and with the ratio of

the periods approximately equal to integer numbers, in case one of the surveys had picked

harmonics or subharmonics of the true period. We used a rather large pairing radius in order

to avoid missing counterparts of our EBs in other catalogues, however, we note that the vast

majority of the counterparts were found to be within a pairing radius of 1′′ (OGLE III: 99%;

MACHO from Faccioli et al. 2007: 57%; MACHO from Derekas et al. 2007: 63%; EROS:

100%).

Twenty-five out of seventy-nine EBs detected in the LMC bar by the first stage of the

EROS microlensing survey (Grison et al. 1995) have a counterpart in our sample of HEBs.

Panel (a) of Figure 4.3 shows the position of those 25 EBs (green dots) on the map of our

1768 HEBs (black dots). The cross-correlation with Derekas et al. (2007) and Faccioli et

al. (2007) catalogues of EBs detected in the LMC by the MACHO survey shows that 797

objects were already known (panel (b) of Fig. 4.3). The cross-correlation with the sample

of 26121 EBs from the OGLE III catalogue (Graczyk et al. 2011), the 1377 EBs and the

156 ellipsoidal stars in the OGLE IV catalogue (Soszynski et al. 2012) showed that 1074

objects were already known (panel (c) of Fig. 4.3). We also cross-matched our sample with

the spectroscopy of massive stars available from the VLT-FLAMES surveys of Evans et al.

(2006,2011), in the NGC 2004, N11 and 30 Doradus regions of the LMC. Eight objects

from our sample have been observed by these surveys: four stars in 30 Doradus by the

VLT-Flames Tarantula Survey (VFTS), two in NGC 2004 and two in N11, as summarized

in Table 4.1. Four of these eight objects have a counterpart in the OGLE III catalogue, one

was observed by the MACHO project, three objects have not been detected before. Optical

60


90 80 70

-72

-70

-68

-66

-64

RA (deg)

-72

-70

-68

-66

-64

90 80 70RA (deg)

Figure 4.3 Panels (a)-(c): spatial distribution of the 1768 HEBs analysed in this study (blackdots) compared with those detected from previous surveys; (a) the first stage of the EROSsurvey (green dots), (b) the MACHO project (red dots), (c) the OGLE III/IV surveys (bluedots). Panel (d) shows the location of the 493 EBs detected only by the EROS-2 survey.Figure is from Muraveva et al. (2014a).

spectroscopy is available for a further five of our detected EBs, from observations with

the AAOmega multi-object spectrograph on the Anglo-Australian Telescope, one of these

objects has not been detected by previous surveys.

To summarize, a total number of 1275 sources in our EROS-2 HEBs sample had pre-

viously been detected by other surveys (OGLE III, OGLE IV, MACHO, EROS, with the

FLAMES and AAOmega spectrographs), whereas 493 were observed only by the EROS-2

survey. The positions of these objects in the LMC are shown in panel (d) of Figure 4.3. As

expected they are mainly located in the outer regions of the LMC.

We also compared our corrected periods with the periods from other catalogues of EBs

(MACHO, OGLE III, OGLE IV). Among the 225 objects for which we corrected the period

163 were also detected by the OGLE III survey, and our corrected periods are in good

agreement (to within 1%) for all but one system. Other 6 and 19 objects with corrected

periods were observed by the OGLE IV and MACHO (Faccioli et al. 2007, Derekas et al.

2007) surveys, respectively. The corrected periods for all of these are in good agreement

with the published values (to within 1%). In conclusion, of the 225 objects for which we

61

4.2. CROSS-CORRELATION WITH OTHER CATALOGUES OF ECLIPSINGBINARIES IN THE LMC

0 2 4 6 8 10

-0.02

-0.01

0

0.01

0.02

0 0.2 0.4 0.6 0.8 1

15.75

15.7

15.65

15.6

0 0.2 0.4 0.6 0.8 1

15.75

15.7

15.65

15.6

0 0.2 0.4 0.6 0.8 1

15.85

15.8

15.75

15.7

0 0.2 0.4 0.6 0.8 1

15.85

15.8

15.75

15.7

Figure 4.4 Left panel: comparison between periods adopted in this study and those inthe OGLE III and OGLE IV catalogues for the 1072 EBs in common. Two objects,namely lm0185l23772 and lm0030n12500, were not included because their OGLE peri-ods differ significantly from our values. Right panels: light curves of lm0185l23772 andlm0030n12500 with the periods used in this thesis work (on the left) and provided by theOGLE III catalogue (on the right). Figure is from Muraveva et al. (2014a).

corrected the periods, 188 were detected by other surveys and our estimates are confirmed

in all but one of these cases (i.e. > 99%).

The left panel of Figure 4.4 shows the comparison of the periods adopted in this thesis

work with those provided by the OGLE III and OGLE IV catalogues for the 1072 objects in

common. Two objects, namely lm0185l23772 and lm0030n12500 are not shown in the plot

because their OGLE III periods are harmonics of the periods derived in this study so they

differ significantly. We checked the light curves of these objects with GRATIS and could

not confirm the periods in the OGLE III catalogue. In particular, for lm0185l23772 (OGLE-

LMC-ECL-09445) we confirmed the period provided by the EROS-2 catalogue (P=4.97

days), whereas for lm0030n12500 (OGLE-LMC-ECL-20762) we determined a new period

(P=1.4998 days) which is one third of the period provided by EROS-2, while OGLE III

determined a period approximately equal to two thirds of the EROS-2 period. The light

curves of these objects are presented on the right panel of Figure 4.4. Apart from these

two objects, the periods adopted in this thesis work and those in the OGLE III catalogue

generally differ by less than 0.03% (left panel of Fig. 4.4).

62


4.3 Characteristics of eclipsing binaries with existing spectroscopy

4.3.1 Cross-matches with the VLT-FLAMES surveys

As already mentioned in Section 4.2, eight HEB systems in our sample have existing optical

spectroscopy from surveys with FLAMES at the VLT (Evans et al. 2006, Evans et al. 2011),

as summarized in Table 4.1. All were detected as binaries in the multi-epoch spectroscopy,

except for VFTS 462 (Dunstall et al. in prep). In addition to the EROS-2 periods, estimates

are also available from the OGLE III data for the four VFTS systems (Graczyk et al., 2011),

with excellent agreement in all cases; the other four systems (in NGC 2004 and the N11

region) are beyond the OGLE III survey area.

Quantitative analysis of the VFTS spectra is still underway, but evolutionary mass es-

timates (of the primaries) of the other systems are available from Hunter et al. (2008);

M = 13M⊙ for both N11-107 and N11-119, and M = 11 and 10M⊙ for NGC 2004-079

and NGC 2004-094, respectively1. Photospheric chemical abundances were presented for

the two systems in NGC 2004 by Hunter et al. (2009), with seemingly unremarkable nitro-

gen abundances. The spectroscopy from the FLAMES surveys was effective in detecting

spectroscopic binaries, but further monitoring is generally required to characterize the or-

bital parameters (e.g., Ritchie et al. 2012). Indeed, spectroscopic monitoring of a subset

of the O-type binaries discovered by the VFTS is now underway (P.I. Sana), and includes

VFTS 061 among its targets.

4.3.2 AAOmega spectroscopy

Optical spectroscopy is available for a further five of our detected EBs, from observations

with the AAOmega multi-object spectrograph on the Anglo-Australian Telescope, obtained

during 2006 February 22-24 (P.I. van Loon). The five targets discussed here were obtained

as part of two fields centred on N11 and 30 Dor. AAOmega is a twin-arm spectrograph

(providing simultaneous blue/red coverage), but only the blue data are discussed here. Both

fields were observed on the first night with the 1700B grating and two central wavelengths

(4100 and 4700 Å), giving coverage of 3765-5015 Å, at a resolution of 1 Å. The 30 Doradus

field was also observed on the second night with the 1500V grating, at a central wavelength

of 4375 Å, providing coverage of 3975-4755 Å, at a resolution of 1.25 Å. These data were

reduced using the AAOmega reduction pipeline and the relevant spectra were rectified and1However, note that these estimates were on the basis of effective temperatures adopted from the spectral

classifications, and the expected uncertainties on these masses is typically 30% (Hunter et al., 2008).

63

4.4. CLASSIFICATION OF ECLIPSING BINARIES

EROS-2 id RA(J2000) DEC(J2000) Period Period Alternative id Spectral type Notes Ref.(deg) (deg) EROS-2 OGLE III

lm0290l18998 73.88709 −66.54208 3.224805 − N11-107 B1-2+Early B SB2 E06lm0290l5213 73.95604 −66.43437 1.791025 − N11-119 B1.5 V SB2 E06lm0344l12773 82.6699 −67.19545 4.952487 − NGC 2004-079 B2 III SB1 E06lm034l21656 82.78869 −67.25619 4.164156 − NGC 2004-094 B2.5 III Binary E06lm0030m4163 84.37804 −69.08817 2.333416 2.333427 VFTS 061 ON8.5III:+O9.7: V: SB2 W14lm0030m3468 84.42029 −69.07812 1.674098 1.674119 VFTS 112 Early B+Early B SB2 E14lm0030m9744 84.46997 −69.16274 1.434738 1.434745 VFTS 189 B0.7: V Binary E14lm0226n24168 84.66296 −69.02808 1.176008 1.176008 VFTS 462 B0.5-0.7 V − E14lm0426m23482 75.07795 −66.06284 2.345573 − − B1: V SB2? . . .lm0294m4825 74.53203 −66.98277 2.97779 2.9778 − B0-0.5 V SB? . . .lm0436l19007 76.28093 −66.19386 3.301123 − − B2 V − . . .lm0020n19615 82.67397 −69.32445 4.585353 4.585031 − B1.5 Ib SB1? . . .lm0031l22987 85.19681 −69.34126 5.413977 5.414011 − B1 III SB2 . . .

Table 4.1 EROS-2 HEBs with existing optical spectroscopy; E06 (Evans et al., 2006); W14(Walborn et al., 2014); E14 (Evans et al. in prep). OGLE III periods are from Graczyk et al.(2011). SB1 and SB2 stand for single- and double-lined spectroscopic binaries, respectively.

co-added.

Spectral classifications for the five systems are presented in Table 4.1, in which we

have employed the same framework as that used by Evans et al. 2014 (in prep.). All five

systems have early B-type spectra (in line with the expectation of these as HEBs), with

morphological evidence for binarity (double-lined and/or asymmetric profiles) in all but

one.

4.4 Classification of eclipsing binaries

Our classification of the EBs was based on both the Fourier analysis (Rucinski 1993,1997

and Maceroni & Rucinski 1999) and the visual inspection of the light curves. As it was

shown in Subsection 1.6.1 the combination of two cosine coefficients of the Fourier de-

composition of EB’s light curves, a2 and a4, could serve as a separator of contact and non-

contact binaries. Namely, the curve described by the relation a4 = a2(0.125 − a2), where

both coefficients are negative, separates the regions of the contact and non-contact bina-

ries on the a2 versus a4 plane (Rucinski, 1993). We adopt the term “contact-binary-like"

systems for all objects passed by the Fourier filter (see Subsection 1.6.1).

By analysis of the Fourier decomposition of the light curves in the REROS passband we

identified the contact-like binaries in our sample. The light curves were not expressed in

magnitudes but in intensity units, relative to the maxima at phases in the range [0.24, 0.26].

Columns from 8 to 13 of Table A.1 (Appendix) present the 6 Fourier coefficients a0 to a5

of the Fourier analysis for the 1768 EBs in our sample.

64


0 0.2 0.4 0.6 0.8 1

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

0.6

0.8

1

1.2

Figure 4.5 Examples of the Fourier fit obtained using 6 harmonics to model the light curveof detached (upper panel) and contact-like (bottom panel) binaries in our sample. Blackdots represent the observational data, red solid lines show the resultant Fourier fits. Six har-monics are clearly not sufficient to reproduce detached systems. Figure is from Muravevaet al. (2014a).

Figure 4.5 shows examples of the resultant fits for both contact-like (lower panel) and

non-contact (upper panel) binary systems. It should be noticed that six harmonics generally

allow very satisfactory fits for contact-like systems, whereas some noticeable differences

arose between the observations and the fitted curves for non-contact binaries, which would

indeed require a much larger number of harmonics (8-10 or more) to be modelled. This is

often due to elliptical orbits, yielding a shift of the secondary minimum from phase 0.5 of

the non-contact systems.

Figure 4.6 shows the position of 1768 EBs in our sample on the a2 versus a4 plane. The

solid line in the figure is the contact locus line defined by Rucinski (1993). We classified

objects located below the line as contact-like binaries (324 sources) and those above as non-

contact binaries (1444 sources). However, being aware that detached and semi-detached

systems could accidentally appear below the locus line due to a bad fit of the light curve, we

visually inspected the light curves of all the objects (324 stars) located below the line; we

discovered eight objects which have light curves without the characteristic form of contact

binaries, so we discarded them. In conclusion, in our analysis a system is classified as

contact-like if it is located below the locus line from Rucinski (1993) on the a2 versus a4

65

4.4. CLASSIFICATION OF ECLIPSING BINARIES

0 -0.1 -0.2

0

-0.05

-0.1

Figure 4.6 Fourier coefficients a2 and a4 of the 1768 HEBs in our sample. The solid curveis described by the relation a4 = a2(0.125 − a2) which, according to Rucinski (1993),separates the regions of contact and non-contact binaries. Objects located below the line areconsidered to be contact systems. Red filled triangles identify objects classified as contactbinaries in the OGLE III catalogue (see text for details). Figure is from Muraveva et al.(2014a).

66


plane and its light curve has the characteristic shape of a contact system.

We compared our classifications with those from the OGLE III catalogue. Out of 1055

objects in common, 48 stars were classified as contact systems in the OGLE III catalogue

(red filled triangles in Figure 4.6). Figure 4.6 shows that the majority of these objects are

in fact located below the locus line traced by Rucinski (1993), while the majority of the

systems classified as non-contact variables by OGLE III are above the curve. However,

eight objects located marginally above the locus line were classified as contact binaries

by OGLE III. We checked their light curves and confirmed that these binaries are indeed

contact-like systems. When including these, the final number of contact-like binaries in

our sample is 324. In contrast, 50 of 1055 objects in common were classified as contact-

like systems by us, but as detached, semi-detched or ellipsoidal systems by OGLE III.

We double checked their light curves, and found that our classification is in disagreement

with OGLE III in some cases. The majority of these objects have low amplitudes so it

is difficult to provide an exact classification by visual inspection of light curves. In the

following analysis we use our classification for those objects, thus our final sample consists

of 324 contact-like binaries and 1444 non-contact systems.

4.5 Period-Luminosity relation of eclipsing binaries

4.5.1 PL relation of eclipsing binaries from the EROS-2 sample

The PL relation of blue, luminous contact systems, observed in the LMC by the MACHO

project, was studied by Rucinski (1999). He suggested the existence of a PL relation at

maximum light in the visual band, but with a large scatter, possibly due to unaccounted

effects of the interstellar extinction (see Section 1.6). Following Rucinski (1999) we have

investigated whether our sample of HEBs follows a PL relation at maximum light using

the red passband photometry of EROS-2 (REROS) and near-infrared photometry in the Ks-

band obtained as part of the VMC survey (Cioni et al. 2011). The latter was used in order

to minimize possible extinction effects.

When this study was performed, the complete multi-epoch dataset was available for

ten LMC tiles, whereas further seven tiles had been observed at least once. These 17 tiles

sample different regions of the LMC from the inner bar to the outer regions.

We have cross-matched our catalogue of 1768 HEBs against the VMC catalogue avail-

able at VSA (observations completed until the 1st of April 2013) for the 17 tiles and found

67

4.5. PERIOD-LUMINOSITY RELATION OF ECLIPSING BINARIES

Figure 4.7 Light curves in the Ks (left panels) and REROS (right panels) passbands ofexample HEBs with a counterpart in the VMC catalogue. P - period (day), N - number ofobservations in the corresponding passband. Figure is from Muraveva et al. (2014a).

68


999 binaries in common using a pairing radius of 1′′. Examples of the Ks and REROS light

curves for some of these binaries are shown in Figure 4.7. The number of phase-points of

the Ks-band light curves varied from a minimum of one for EBs located in tiles with incom-

plete observations to a maximum of over 30 phase points for EBs located in regions where

different tiles overlap. Furthermore, the EBs in our sample are relatively bright sources.

Therefore the shallow VMC epochs, for which the integration time of observation is half

that for deep epochs, or epochs not meeting the original quality criteria (e.g., seeing, etc.)

were enough to measure the EBs thus increasing the number of available phase-points.

The REROS and Ks magnitudes at maximum light of the binaries that have a VMC

counterpart are presented in Table A.2 (Appendix). In order to better determine the Ks-band

magnitudes at maximum light, we performed an additional analysis of the light curves with

GRATIS, for those HEBs which have 13 or more good-quality observations. The left panel

of Figure 4.8 shows the PL distribution in the REROS band of the 999 EBs with a VMC

counterpart, whereas the right panel shows their PL distribution in the Ks band. In both

figures red open circles identify the sources which we classified as contact-like systems. The

contact binaries for which we have 13 or more Ks-band epochs (and for which maximum

magnitudes were determined with GRATIS) are highlighted in green. Unfortunately, the

use of a more robust method to determine the Ks magnitude at maximum light does not

decrease the scatter. Both the optical and near-infrared PL distributions exhibit a very large

dispersion, which is of the same order of the scatter observed in the PL relation originally

used by the EROS-2 team to extract the candidate CCs from the EROS-2 general catalogue

of LMC variables (see right panel of Fig. 2.3). Thus, a PL relation for HEBs doesn’t seem

to exist.

4.5.2 PL relation of eclipsing binaries from the OGLE III catalogue

In order to study the PL relation of contact binaries in a more general sample and over

a larger range of periods we have used the OGLE III catalogue of EB stars published by

Graczyk et al. (2011). We extracted all the objects which were classified as contact bina-

ries in the Graczyk et al. (2011) catalogue. Among them we selected objects with VMC

counterparts and, with both V and I magnitudes from OGLE III, giving 563 objects in to-

tal. Twenty-five of these sources have their counterparts in our sample of HEBs from the

EROS-2 catalogue and were already discussed in Section 4.5.1. To account for extinction

we used the LMC reddening maps derived by Haschke et al. (2011) on the basis of OGLE III

69


0 0.5 1

18

16

14

0 0.5 1

18

16

14

Figure 4.8 PL distribution in the REROS (left panel) and Ks (right panel) passbands of999 HEBs that have a counterpart in the VMC catalogue (black dots). Red open circles areobjects which we classified as contact binaries. Green filled circles are 90 contact EBs forwhich we have 13 or more epochs in the Ks light curves. Figure is from Muraveva et al.(2014a).

data. To compute extinction values in the various bands we used the relations from Schlegel

et al. (1998) and Cardelli et al. (1989), these were then applied to correct each source.

The reddening corrected V0, (V − I)0 CMD of contact binaries from the OGLE III

catalogue is shown in Figure 4.9. Contact binaries are located in two regions in the CMD:

HEBs which contain MS stars or blue giants have (V − I)0 < 0.3 mag, whereas EBs with a

red giant component have (V − I)0 ≥ 0.3 mag. The corresponding PL distributions in the

I0 and Ks,0 bands are presented in Figure 4.10. In the figures HEBs are indicated with black

dots and binary systems containing red giants are indicated with red triangles. For 164 EBs

with a red giant component, which have 13 or more good-quality epochs from the VMC

survey, we analysed the light curves with GRATIS in order to determine the Ks magnitude

at maximum light with a good accuracy. On the right panel of Fig. 4.10 we have highlighted

these objects with green triangles. While contact HEBs from the OGLE III sample do not

distribute along a PL sequence, contact binaries containing red giant components seem to

follow at least one, maybe two, different PL sequences.

To further investigate this point we restricted our analysis to 164 objects with carefully

determined Ks maximum magnitudes (green triangles on the right panel of Fig. 4.10). Their

PL distribution is shown in Figure 4.11. As it could be seen, there are 11 objects with short

70


-1 0 1 2 3

20

18

16

14

12

Figure 4.9 CMD of 563 contact binary stars which have V and I (OGLE III) and Ks (VMC)magnitudes. Black dots are objects with (V − I)0 < 0.3 mag and red triangles are objectswith (V − I)0 ≥ 0.3 mag. The dashed line corresponds to (V − I)0 = 0.3 mag. Figure isfrom Muraveva et al. (2014a).

-1 0 1 2 3

20

18

16

14

12

-1 0 1 2 3

20

18

16

14

12

Figure 4.10 PL distribution at I0 maximum (left panel) and at Ks,0 maximum (right panel)of the 563 contact binaries shown in Fig. 4.9. Black dots are objects with (V − I)0 < 0.3mag, red triangles are objects with (V − I)0 ≥ 0.3 mag of which those with 13 or moreepochs in the Ks-band are marked in green. Figures are from Muraveva et al. (2014a).

71


-1 0 1 2 3

18

16

14

12

Figure 4.11 PL distribution of contact binaries containing red giant components. Blue opencircles are candidate HEBs falling in the region of binaries with red giant components (theirerrors are smaller than the size of the circles), red and black dots represent EBs whichdeviate less (red) and more (black) than 3σ from a linear regression, respectively. The lineis the weighted linear fit obtained from the objects marked in red. Figure is from Muravevaet al. (2014a).

72


periods which do not follow any PL sequence (blue open circles in Fig. 4.11). We checked

the position of these objects in the CMD (Fig. 4.9) and found that they are located in the

border region between HEBs and binaries with red giant components. Since these objects

do not follow the PL sequence and could be HEBs, we discarded them from the following

analysis.

For other 153 EBs we computed a weighted linear regression through the data by pro-

gressively discarding objects which deviate more than 3σ from the linear regression. The

majority of contact systems with carefully determined Ks maximum magnitudes (red dots

in Figure 4.11) appear to follow the relation :

Ks,0 = (−2.888 ± 0.096)log(P ) + (20.139 ± 0.171) (4.1)

with rms=0.406 mag.

In Figure 4.11 we have highlighted objects located more than 3σ from the PL distri-

bution with black dots. Some of them seem to follow a PL sequence parallel to the one

described by Eq. 4.1 and located ∼ 1 mag fainter than the previous one.

To summarize, HEBs do not follow any PL relation while the existence of red giant

PL sequence(s) (at least, one) seems quite clear and, as shown by Fig. 4.10, this relation

appears to be narrower in the Ks passband. However, the large scatter makes it impossi-

ble to use these sequences any further. On the other hand, that red giants follow multi-

ple PL relations was already reported in many studies (Wood et al. 1999, Soszynski et al.

2004, Derekas et al. 2006). Wood et al. (1999) were the first to recognize five different

PL-sequences: A, B and C, occupied by pulsating red giants, D composed by stars that

have long secondary periods (LSPs), and sequence E, containing red giants in contact EBs

and ellipsoidal variables. Soszynski et al. (2004) showed that a PL relation of ellipsoidal

variables could be well described by a simple model using the Roche-lobe geometry and

that sequences E and D merge at specific luminosities. Derekas et al. (2006) presented a

period-luminosity-amplitude analysis of 5899 red giant and binary stars in the LMC from

the MACHO database and discovered that the PL sequence of binaries is composed only by

contact EBs, while detached and semi-detached systems are spread everywhere in the PL

plane. Moreover, they concluded that sequence E, is located at periods a factor two greater

and overlaps with the sequence of LSPs (sequence D). In our study we confirm the existence

of a PL sequence containing contact binaries with red giant components (Eq. 4.1) and find

evidence for a possible additional PL sequence of contact binaries located ∼ 1 mag fainter.

73

4.6. STRUCTURE OF THE LMC FROM “HOT” ECLIPSING BINARIES ANDCLASSICAL CEPHEIDS

Furthermore, thanks to the depth achieved by the VMC data, we are able to extend the PL

relation of contact binaries, containing red giants, to Ks ∼ 18 mag, roughly two magnitudes

fainter than in Derekas et al. (2006). The existence of PL relation(s) for red giant EBs and

its absence for HEBs could be explained by intrinsic differences occurring between the two

samples. In the case of contact systems with red giants the total luminosity of the binary

system is dominated by one component - the red giant star, the luminosity of the second

component being negligible. On the contrary, for HEBs the ratio of luminosities of the two

O-B components could vary significantly. Therefore, the scatter of the PL relation of bi-

naries with O-B components is expected to be much larger than the scatter of the PLKs

relation of contact systems with a red giant component.

4.6 Structure of the LMC from “hot” eclipsing binaries and Clas-sical Cepheids

The distribution of the LMC CCs and HEBs is presented in Figure 4.12. As it was discussed

in the previous sections, we suggested that the EROS-2 candidate CCs with colour 0.2 ≤

(BEROS−REROS) ≤ 1 mag are bona-fide CCs. The upper-left panel of Figure 4.12 shows

the distribution of CCs in the LMC. CCs are relatively young objects (50-200 Myr), so they

trace the bar of the galaxy and the spiral arm. In the upper-right panel of Figure 4.12 the

distribution of 1768 HEBs from our sample is shown. It differs from the distribution of

CCs as it could be seen on the bottom-left panel of Figure 4.12 . HEBs are more clustered,

do not follow the entire bar and locate in the regions of recent star formation activity, such

as 30 Doradus and Constellation III, and supergiant shells (SGS 11, SGS 7, SGS 3, SGS

12 and others). On the bottom-right panel of Figure 4.12 the distribution of objects which

were classified as contact-like binary stars is shown. It is similar to the distribution of the

whole sample of EBs. These results are in agreement with the Star Formation History of the

LMC. Harris & Zaritsky (2009) found that the bar of the LMC had partially active episodes

of star formation 5 Gyr, 500 Myr and 100 Myr ago. CCs in the bar were formed during the

last episode of star formation activity 100 Myr years ago, while the activity at 12 Myr is

dominated by 30 Doradus and the Constellation III regions, which are not related to the bar

and where the majority of binary stars from our sample is concentrated.

74


-75

-70

-65

90 80 70

-75

-70

-65

90 80 70

-75

-70

-65

90 80 70

Figure 4.12 Distribution of CCs (black dots), HEBs (red dots) and contact-like binaries(blue dots) in the LMC.

75

Chapter 5

RR Lyrae stars in the VMC tile LMC5_5

RR Lyrae stars make useful distance indicators because of the existence of a MV − [Fe/H]

relation in the visual band and of a PLZ relation in the infrared passbands (see Subsec-

tion 1.5.2). In this chapter we present results of the analysis of 71 RR Lyrae stars located

in tile LMC 5_5, close to the bar of the galaxy, for which individual spectroscopically

determined [Fe/H] abundances exist in the literature (Gratton et al., 2004). Combining the

metallicities of these stars, precise periods from the OGLE III catalogue and multi-epoch Ks

photometry from the near-infrared VISTA survey of the Magellanic Clouds system (Cioni

et al., 2011) we derive a new near-infrared PLKsZ relation for RR Lyrae variables. In order

to check the impact of Gaia (Section 1.2) on the determination of the zero-points of the RR

Lyrae PLKsZ and MV − [Fe/H] relations, we simulate Gaia parallaxes for 25 RR Lyrae

stars in the Milky Way.

5.1 Data for RR Lyrae stars in the bar of the LMC

Optical photometry for the LMC RR Lyrae stars discussed in this chapter was obtained

using the Danish 1.54 meter telescope, the 3.6 m, and the VLT ESO telescopes, at two

different sky positions, hereafter called fields A and B. Both are located in tile LMC 5_5,

close to the bar of the galaxy (Clementini et al. 2003, Di Fabrizio et al. 2005). As a result,

accurate B, V and I light curves tied to the Johnson-Cousins standard system and pulsation

characteristics (period, epoch of maximum light, amplitudes and mean magnitudes; Di Fab-

rizio et al. 2005) for 125 RR Lyrae stars were obtained. Low-resolution spectra for 98 of

these RR Lyrae stars were collected by Gratton et al. (2004) using the FORS1 (FOcal Re-

ducer/low dispersion Spectrograph) instrument mounted at the ESO VLT. They were used

77

5.1. DATA FOR RR LYRAE STARS IN THE BAR OF THE LMC

to derive metal abundances by comparing the strength of the Ca II K line with that of the

H lines (Preston, 1959). For the calibration of the method, four Galactic globular clusters

with metallicities in the range [−2.06; −1.26] dex were used. The obtained metallicities are

tied to a scale, which is, on average, 0.06 dex more metal-rich than the Zinn & West (1984)

metallicity scale.

We cross-matched the sample of 98 RR Lyrae variables with known metallicities against

the catalogue of RR Lyrae stars observed by the OGLE III survey (Soszynski et al., 2009).

The OGLE III catalogue contains information about the position, photometric and pulsation

properties of 24906 RR Lyrae stars in the LMC (see Subsection 2.4.2). We found that,

respectively, 94, 2 and 2 objects are cross-identified with sources in the OGLE III catalogue

within a pairing radius of 1′′, 3′′ and 7′′. The 2 stars with a counterpart at more than 5′′

are OGLE-LMC-RRLYR-10345 and OGLE-LMC-RRLYR-10509; for these two stars we

checked both the OGLE III finding charts and Gratton et al. (2004) Figure 5 (field B1)

in order to understand if they are affected by any problem. Star OGLE-LMC-RRLYR-

10345 is an isolated lightly elongated star without any clear blending problem, while star

OGLE-LMC-RRLYR-10509 is very close to another source possibly making more difficult

to accurately locate the star center. Considering that Gratton et al. (2004) and OGLE III

periods for these 2 stars agree within 0.5%, we kept these stars in our sample.

We compared the periods of the 98 RR Lyrae stars provided by Di Fabrizio et al. (2005)

and those in the OGLE III catalogue (Soszynski et al., 2009). For 96 objects the periods

agree within ∼ 2%, while for two objects periods differ significantly. For star A6332 the

difference is ∼ 25% and for star A5148 it is ∼ 37% (star identifications are from Di Fabrizio

et al. 2005). Moreover, star A5148 has been classified as a first-overtone RR Lyrae star in

the OGLE III catalogue, and as a fundamental-mode RR Lyrae by Di Fabrizio et al. (2005).

Since accurately estimated periods and classifications play a key role in the current study,

we decided to discard these two objects from the following analysis.

Seven objects (B2811, B4008, B3625, B2517, A2623, A2119, A10360) in our sample

are classified as RRc by Di Fabrizio et al. (2005) and as RRe in the OGLE III catalogue.

We removed them from our analysis because of the uncertain classification. Furthermore,

since one of the main purposes of the current research is to study the PLKsZ relation of

RR Lyrae stars of ab- and c-types we also discarded seven objects, which were classified as

double-mode RR Lyrae stars (RRd) by Di Fabrizio et al. (2005): A7137, A8654, A3155,

A4420, B7467, B6470 and B3347. This left us with a final sample of 61 RRab and 21

78

CHAPTER 5. RR LYRAE STARS IN THE VMC TILE LMC 5_5

RRc stars, which have counterparts in the OGLE III catalogue. The period search for the

RR Lyrae stars in the OGLE III catalogue was performed using an algorithm based on

the Fourier analysis of the light curves (Soszynski et al., 2009). The uncertainties in the

OGLE III periods for the 82 RR Lyrae stars in our sample are declared to be less than

5× 10−6 days. Therefore we used the periods provided by the OGLE III catalogue in order

to fit the PLKsZ relation, and do not consider errors in the periods since they are negligible

in comparison to the other uncertainties.

In order to derive mean Ks magnitudes for the RR Lyrae stars in our sample we used

data from the VMC survey (Cioni et al. 2011, see Subsection 2.4.3). The majority of RR

Lyrae stars in our sample are located within the VMC tile LMC 5_5. PSF photometry of the

time-series data for this tile was performed on the homogenised epoch-tile images (Rubele

et al., 2012) using the IRAF Daophot (Stetson et al., 1990) packages. On each epoch-

tile image the PSF model was created using 2500 stars uniformly distributed, finally the

Daophot ALLSTAR routine was used to perform the PSF photometry on all epoch images

and time-series catalogues were correlated within a tolerance of one arcsec. We have cross-

matched our sample of 82 RR Lyrae stars against the PSF photometry catalogue of tile LMC

5_5. VMC counterparts for 71 objects were found within a pairing radius of 1′′. For 70 of

them we have 13 epochs in the Ks-band, and for one object (B4749) we have observations

only in 6 epochs.

We determined mean Ks magnitudes using Ks-band light curve templates for RR Lyrae

stars from Jones et al. (1996) to fit the 13 different epochs (6 for B4749) available for

the 71 stars. All available epochs were used in the present analysis. However, checks are in

progress to verify that photometric errors and varying observing conditions of the individual

epochs do not affect the derived PLKsZ relation. Jones et al. (1996) developed one Ks-band

light curve template for RRc variables and four different templates for RRab stars, the latter

vary depending on the Johnson V amplitude of pulsation (VJ ). Di Fabrizio et al. (2005)

provides amplitudes in the V passband (hereinafter, Amp(V )) for the majority but not all

the 71 RR Lyrae stars in our sample. Specifically, Amp(V ) of star A26715 is missing and

for five other objects (B6798, A16249, B1907, A28066, B24089) Di Fabrizio et al. (2005)

provided more than one value of amplitude, likely because these objects have photometric

problems, e.g. blends. On the other hand, the OGLE III catalogue provides Cousins I band

(IC) amplitudes [Amp(I)] for all the variables in our list. We have transformed them to VJ

79


Figure 5.1 Distribution of the differences between the V -band amplitudes provided by DiFabrizio et al. (2005) and those derived by transforming to Amp(V ) the Amp(I) values inthe OGLE III catalogue.

amplitudes using the relation by Di Criscienzo et al. (2011):

Amp(V ) = 1.58×Amp(I) (5.1)

and have compared the derived Amp(V ) values with those published by Di Fabrizio et al.

(2005). This comparison is shown in Fig.5.1. The distribution of amplitude differences is

symmetric around the value zero and for the vast majority of sources is smaller than 0.1

mag. Only in a few extreme cases this difference is as large as 0.31 mag. Given the higher

completeness of OGLE III dataset, in order to fit templates to the light curves of the 71 RR

Lyrae stars in our sample we have thus adopted OGLE III epochs of maximum light and the

IC amplitudes transformed to VJ as discussed above. We also corrected for any phase shift

between template and data points when necessary. Examples of the Ks-band light curves of

RR Lyrae stars in our sample and their fitting templates are presented in Fig. 5.2.

In order to test the robustness of our determination of the Ks mean magnitudes using

templates, for a number of RR Lyrae stars with evenly sampled light curves mean Ks mag-

nitudes were also derived by Fourier fitting the light curves with GRATIS period search

package. This analysis showed that the Ks mean magnitudes derived with the GRATIS are

consistent within the errors with those obtained by applying templates, thus supporting our

80


Figure 5.2 Examples of the Ks-band light curves of RR Lyrae stars in our sample. Identifi-cation numbers are from Di Fabrizio et al. (2005), periods are from the OGLE III catalogue(Soszynski et al., 2009) and are given in days. Solid (red) lines are best fitting templates.

81


estimates of mean Ks magnitudes via template fitting.

After deriving the Ks mean magnitudes we performed the dereddening procedure. Clemen-

tini et al. (2003) estimated reddening values of E(B−V ) = 0.116±0.017 and 0.086±0.017

mag in fields A and B, respectively, using the method from Sturch (1966) and the colours

of the edges of the instability strip defined by the RR Lyrae variables. Applying the co-

efficients from Cardelli et al. (1989) of AK/AV = 0.114 and assuming a ratio of total to

selective absorption of RV = 3.1, we estimated the extinction in the Ks-band as:

AKs = 0.35 × E(B − V ) (5.2)

Table 5.1 summarizes the properties of the sample of 71 RR Lyrae stars. The first two

columns of the table give the identification of the stars in Di Fabrizio et al. (2005) and in the

OGLE III catalogue, respectively. The table also shows coordinates and classification of the

stars from the OGLE III catalogue, metallicity with errors from Gratton et al. (2004) and

dereddened mean Ks magnitudes, determined by template fitting, along with their errors.

82


Star

OG

LEID

RA

DEC

Type

[Fe/

H]

σ[Fe/

H]

P⟨K

s,0⟩

σ⟨K

s,0⟩

(J20

00)

(J20

00)

(dex

)(d

ex)

(day

s)(m

ag)

(mag

)A

2866

5O

GLE

-LM

C-R

RLY

R-1

2944

5:22

:06.

55-7

0:27

:55.

6c

-0.6

30.

240.

3008

299

18.4

690.

014

A78

64O

GLE

-LM

C-R

RLY

R-1

3857

5:23

:39.

25-7

0:31

:38.

1c

-1.3

60.

220.

3129

458

18.5

040.

014

B49

46O

GLE

-LM

C-R

RLY

R-1

0621

5:18

:11.

08-7

0:59

:35.

6c

-1.1

10.

250.

3130

142

18.3

690.

008

A26

36O

GLE

-LM

C-R

RLY

R-1

3548

5:23

:09.

09-7

0:39

:08.

1c

-1.6

10.

290.

3154

437

18.5

580.

013

A88

37O

GLE

-LM

C-R

RLY

R-1

3326

5:22

:45.

70-7

0:30

:14.

3c

-1.5

20.

220.

3165

579

18.5

840.

011

A86

22O

GLE

-LM

C-R

RLY

R-1

3164

5:22

:28.

93-7

0:30

:35.

9c

-1.4

40.

280.

3212

334

18.4

050.

010

A72

31O

GLE

-LM

C-R

RLY

R-1

3680

5:23

:22.

42-7

0:32

:35.

4c

-1.4

60.

260.

3228

047

18.2

250.

011

A22

34O

GLE

-LM

C-R

RLY

R-1

3479

5:23

:01.

47-7

0:39

:44.

4c

-1.5

30.

180.

3228

060

18.3

230.

009

B47

49O

GLE

-LM

C-R

RLY

R-1

0406

5:17

:49.

73-7

1:00

:01.

4c

-1.4

50.

160.

3267

353

18.3

640.

014

A43

88O

GLE

-LM

C-R

RLY

R-1

2614

5:21

:31.

67-7

0:36

:46.

3c

-1.3

30.

270.

3417

737

18.3

950.

012

A10

113

OG

LE-L

MC

-RR

LYR

-140

465:

24:0

0.38

-70:

28:0

6.1

c-1

.52

0.25

0.35

0661

818

.237

0.01

2B

6255

OG

LE-L

MC

-RR

LYR

-101

115:

17:1

7.88

-70:

57:2

6.4

c-1

.52

0.16

0.35

3559

618

.297

0.01

0B

4179

OG

LE-L

MC

-RR

LYR

-101

425:

17:1

9.95

-71:

01:0

2.1

c-1

.53

0.27

0.35

4523

218

.150

0.00

9A

8812

OG

LE-L

MC

-RR

LYR

-131

505:

22:2

6.44

-70:

30:1

9.1

c-1

.23

0.24

0.35

4966

018

.254

0.01

3A

2671

5O

GLE

-LM

C-R

RLY

R-1

2593

5:21

:29.

33-7

0:29

:23.

4c

-1.3

90.

180.

3569

006

18.2

910.

012

A20

24O

GLE

-LM

C-R

RLY

R-1

3572

5:23

:11.

02-7

0:40

:03.

3c

-1.6

20.

260.

3590

534

18.2

440.

008

B61

64O

GLE

-LM

C-R

RLY

R-1

0612

5:18

:10.

17-7

0:57

:30.

7c

-1.8

80.

220.

3744

821

18.0

270.

008

A27

697

OG

LE-L

MC

-RR

LYR

-130

125:

22:1

4.03

-70:

28:3

5.0

c-1

.33

0.25

0.38

2570

018

.030

0.01

1A

1945

0O

GLE

-LM

C-R

RLY

R-1

3841

5:23

:37.

95-7

0:34

:06.

7ab

-0.7

60.

130.

3979

182

18.5

500.

011

B70

64O

GLE

-LM

C-R

RLY

R-1

0708

5:18

:18.

63-7

0:55

:58.

7c

-2.0

30.

200.

4004

744

17.9

970.

009

B69

57O

GLE

-LM

C-R

RLY

R-1

0702

5:18

:18.

08-7

0:56

:08.

7c

-1.4

80.

180.

4047

399

18.0

500.

008

B23

502

OG

LE-L

MC

-RR

LYR

-105

095:

18:0

0.25

-70:

54:3

1.0

ab-1

.55

0.14

0.47

2468

118

.249

0.00

8A

3061

OG

LE-L

MC

-RR

LYR

-137

045:

23:2

5.18

-70:

38:2

8.9

ab-1

.26

0.12

0.47

4441

018

.324

0.00

9B

1081

1O

GLE

-LM

C-R

RLY

R-1

0684

5:18

:16.

01-7

1:04

:27.

0ab

-1.4

20.

200.

4760

753

18.2

380.

009

B34

00O

GLE

-LM

C-R

RLY

R-1

0072

5:17

:14.

51-7

1:02

:26.

6ab

-1.4

50.

240.

4852

148

18.3

440.

011

A73

25O

GLE

-LM

C-R

RLY

R-1

3855

5:23

:39.

13-7

0:32

:24.

8ab

-1.1

80.

260.

4864

544

18.2

340.

009

B30

33O

GLE

-LM

C-R

RLY

R-1

0659

5:18

:14.

04-7

1:03

:00.

5ab

-1.2

60.

210.

4986

975

18.0

820.

008

B20

55O

GLE

-LM

C-R

RLY

R-1

0108

5:17

:17.

44-7

1:04

:50.

2ab

-1.7

00.

230.

5207

746

18.2

530.

010

A26

525

OG

LE-L

MC

-RR

LYR

-128

115:

21:5

2.50

-70:

29:2

8.7

ab-1

.41

0.22

0.52

2502

918

.140

0.00

8A

7211

OG

LE-L

MC

-RR

LYR

-130

925:

22:2

1.17

-70:

32:4

3.9

ab-1

.33

0.19

0.52

2685

718

.170

0.00

8

83

5.1. DATA FOR RR LYRAE STARS IN THE BAR OF THE LMCA

2767

OG

LE-L

MC

-RR

LYR

-136

345:

23:1

7.75

-70:

38:5

5.9

ab-1

.37

0.08

0.53

2587

118

.069

0.01

2B

2408

9O

GLE

-LM

C-R

RLY

R-1

0345

5:17

:43.

51-7

0:54

:02.

7ab

-1.4

80.

160.

5580

613

18.0

420.

009

A87

88O

GLE

-LM

C-R

RLY

R-1

3678

5:23

:22.

41-7

0:30

:14.

6ab

-1.6

10.

210.

5591

710

18.1

770.

011

A63

98O

GLE

-LM

C-R

RLY

R-1

3294

5:22

:40.

76-7

0:33

:50.

2ab

-1.4

00.

300.

5619

466

17.9

550.

008

A72

47O

GLE

-LM

C-R

RLY

R-1

3708

5:23

:25.

58-7

0:32

:33.

4ab

-1.3

80.

210.

5621

512

18.0

250.

008

A25

301

OG

LE-L

MC

-RR

LYR

-126

385:

21:3

4.00

-70:

30:2

4.5

ab-1

.58

0.27

0.56

3114

618

.279

0.00

9A

1538

7O

GLE

-LM

C-R

RLY

R-1

2603

5:21

:30.

43-7

0:37

:11.

3ab

-1.8

10.

120.

5635

914

18.0

370.

009

B22

917

OG

LE-L

MC

-RR

LYR

-107

135:

18:1

9.10

-70:

54:5

6.1

ab-1

.29

0.16

0.56

4680

318

.159

0.00

8A

9245

OG

LE-L

MC

-RR

LYR

-135

365:

23:0

7.67

-70:

29:3

6.5

ab-1

.27

0.18

0.56

7876

318

.043

0.00

9A

1289

6O

GLE

-LM

C-R

RLY

R-1

3330

5:22

:46.

15-7

0:38

:54.

9ab

-1.5

30.

100.

5719

281

18.1

470.

008

A76

09O

GLE

-LM

C-R

RLY

R-1

3941

5:23

:48.

39-7

0:32

:00.

3ab

-1.6

30.

110.

5724

984

18.0

790.

008

B74

42O

GLE

-LM

C-R

RLY

R-1

0082

5:17

:15.

73-7

0:55

:26.

8ab

-1.5

80.

110.

5740

274

18.0

170.

008

A25

362

OG

LE-L

MC

-RR

LYR

-138

485:

23:3

8.53

-70:

30:0

8.5

ab-1

.39

0.15

0.57

8794

418

.027

0.00

8B

1907

OG

LE-L

MC

-RR

LYR

-106

385:

18:1

2.36

-71:

04:5

9.5

ab-1

.70

0.26

0.58

1828

317

.930

0.00

8A

4974

OG

LE-L

MC

-RR

LYR

-133

725:

22:5

1.26

-70:

35:4

7.7

ab-1

.36

0.10

0.58

2043

017

.996

0.00

9B

6798

OG

LE-L

MC

-RR

LYR

-100

445:

17:1

1.37

-70:

56:3

2.6

ab-1

.40

0.23

0.58

2261

017

.926

0.01

1B

1444

9O

GLE

-LM

C-R

RLY

R-0

9999

5:17

:05.

37-7

1:01

:40.

9ab

-1.7

00.

130.

5822

854

18.1

220.

010

A94

94O

GLE

-LM

C-R

RLY

R-1

3354

5:22

:49.

26-7

0:29

:13.

5ab

-1.6

90.

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.718

0.01

0

84

CHAPTER 5. RR LYRAE STARS IN THE VMC TILE LMC 5_5A

8720

OG

LE-L

MC

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565:

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0.19

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0.65

6160

217

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7477

OG

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700.

008

Tabl

e5.

1:Pr

oper

ties

ofth

e71

RR

Lyra

est

ars

inth

eV

MC

tile

LMC

5_5

used

tode

rive

ane

wPLK

sZ

rela

tion

(Col

umn

1:Id

entifi

catio

nof

the

star

from

DiF

abriz

ioet

al.(

2005

);C

olum

n2:

Iden

tifica

tion

from

the

OG

LEII

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talo

gue

(Sos

zyns

kiet

al.,

2009

);C

olum

n3:

Rig

htas

-ce

nsio

n(O

GLE

);C

olum

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linat

ion

(OG

LE);

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umn

5:R

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rae

type

;Col

umn

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etal

licity

from

Gra

tton

etal

.(20

04);

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umn

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-ro

rofm

etal

licity

from

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tton

etal

.(20

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umn

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riod

(OG

LE);

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umn

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tude

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the

VM

Csu

rvey

;Col

-um

n10

:Err

orof

the

mea

nK

sm

agni

tude

).

85

5.2. PLKSZ RELATION OF RR LYRAE STARS IN THE LMC

5.2 PLKsZ relation of RR Lyrae stars in the LMC

5.2.1 Method

Using the dereddened mean Ks magnitudes of the 71 RR Lyrae stars derived as described

in Section 5.1, spectroscopically determined metallicities from Gratton et al. (2004) and ac-

curately estimated periods from the OGLE III catalogue (with RRc stars "fundamentalized"

by adding 0.127 to the logarithm of the period) we can now fit the PLKsZ relation. The fit

was performed using a Bayesian fitting approach developed by Max Palmer, PhD student of

the University of Barcelona. This method takes into account potentially significant intrinsic

dispersion of the data, not-negligible errors in two dimensions (Ks and [Fe/H]) and the pos-

sibility of inaccuracy in the formal error estimates (e.g. in the determination of the precision

metallicity estimates). The detailed description of the method is presented in Muraveva et

al. (2014b, submitted to AJ).

By applying this method we found the following relation between periods of pulsation,

metallicities and mean apparent Ks magnitudes determined with templates:

Ks,0 = (−2.70 ± 0.22)logP + (0.03 ± 0.06)[Fe/H]

+ (17.44 ± 0.05) (5.3)

The intrinsic dispersion of the relation is found to be 0.09 mag.

The projections of the PLKsZ relation (Eq. 5.3) on the Log(P )−Ks and Ks − [Fe/H]

planes is shown in Figure 5.3. The grey lines in the figure are lines of equal metallicity

(top) or equal period (bottom). The method finds the relation (values of A, B, and C for the

relation Ks = A logP+B [Fe/H]+C) in three dimensions (logP, Ks, and [Fe/H]). So each of

the grey lines in the top plot are Ks = A logP+B [Fe/H]+C for the full range of periods, at

the metallicity of each star (one line per star). Thus, by following the line up and down it

is seen how Ks changes with period at some specific metallicity. The lines do not always

cross the points on the diagram because the line is the result of the fit, and the points are

affected by errors and intrinsic dispersion so may be above or below the fit. In the bottom

plot the lines are Ks = A logP+B [Fe/H]+C for the full range of metallicity with logP taken

from each star.

It is worth noting that we find a very small dependence of the Ks magnitude on the

metallicity. However, the metal abundance range spanned by our RR Lyrae stars does not

86


Figure 5.3 Projections of the PLKsZ relation (given in Eq. 5.3) on the Log(P) versus Ks

(top panel) and Ks versus [Fe/H] (bottom panel) planes. Grey lines represent lines of equalmetallicities (top panel) and periods (bottom panel).

reach the highest values (up to solar and supersolar) observed in the MW bulge and disk RR

Lyrae populations.

5.2.2 Zero-point of the PLKsZ relation

To use the derived PLKsZ relation for determining distances it is necessary to calibrate

its zero-point. This can be done in a number of different ways. In this study we follow

two different approaches: the first one is based on adopting a value for the distance of the

LMC; in the second approach we use the absolute magnitudes of Galactic RR Lyrae stars

for which trigonometric parallaxes have been measured with the HST/FGS (Benedict et al.,

2011). Both approaches have their advantages and disadvantages, we discuss them in the

following sections.

87

5.2. PLKSZ RELATION OF RR LYRAE STARS IN THE LMC

Zero-point based on the LMC distance

The measure of the distance to the LMC has been the subject of many studies (see Sec-

tion 2.3). A recent determination of direct distances to eight long-period EBs in the LMC

was presented by Pietrzynski et al. (2013) and claimed to be accurate to ∼ 2%: DLMC =

49.97 ±0.19 (stat) ± 1.11 (syst) kpc, corresponding to the distance modulus (m−M)0 =

18.494 ± 0.049 mag.

The RR Lyrae stars in our sample are located in a relatively small area close to the

center of the LMC bar. Neglecting depth/projection effects they can be considered as being

all at the same distance from us and close to late-type EBs (Pietrzynski et al., 2013), which

are all located relatively close to the barycentre of the LMC. In the following analysis we

adopted for the distance modulus of the LMC the value published by Pietrzynski et al.

(2013) and subtracted this value from the dereddened mean Ks apparent magnitudes of

our 71 RR Lyrae stars to derive absolute Ks magnitudes (MK ). Then by applying the

technique described in Section 5.2.1 we derived the relation between absolute magnitudes,

periods and metallicities obtaining for the zero-point the value of: −1.05 ± 0.05 mag (see

column 2 of Table 5.2). In using the late-type EBs to calibrate the RR Lyrae PLKsZ

relation we have implicitly assumed that RR Lyrae stars and EBs are at same distance from

us. However, when pushing for distance comparisons at a few percent level the effects

of sample size, spatial distribution, depth and geometric projection become important and

properly accounting for the internal structure of the LMC may become necessary (see e.g.

Fig. 2.1 for different features of the LMC structure traced by CCs, RR Lyrae stars and

HEBs).

Zero-point based on trigonometric parallaxes of Galactic RR Lyrae stars

In order to obtain an estimate of the PLKsZ relation zero-point which is independent from

the distance to the LMC and, in turn, be able to measure the distance to this galaxy from the

PLKsZ relation, it is necessary to know the RR Lyrae absolute magnitude with reasonable

accuracy. Trigonometric parallaxes remain the only direct method to measure distances and

hence derive absolute magnitudes (see Section 1.1). Benedict et al. (2011) derived absolute

trigonometric parallaxes for five Galactic RR Lyrae stars (RZ Cep, XZ Cyg, SU Dra, RR

Lyr and UV Oct) with the HST/FGS. With these parallaxes the authors estimated absolute

magnitudes in the K and V passbands, corrected for interstellar extinction and Lutz-Kelker-

Hanson bias (hereinafter LKH, Lutz & Kelker 1973, Hanson 1979). Absolute magnitudes

88


Relation ZP from DLMC ZP from Benedict et al. (2011)MK = (−2.70± 0.22)logP + (0.03 ± 0.06)[Fe/H]Har + ZP (−1.05 ± 0.05) (−1.27± 0.08)

Table 5.2 Absolute calibration of the new PLKsZ relation.

in the Ks-band, periods and metallicities from Benedict et al. (2011), and the slopes of

the relation derived in Eq. 5.3 were used in order to determine a zero-point from each

of these five MW RR Lyrae stars. The metallicities in Benedict et al. (2011) are in the

Zinn & West metallicity scale and were converted to the metallicity scale in Gratton et

al. (2004) by adding 0.06 dex. The logarithm of the period of the RRc star RZ Cep was

"fundamentalized" by adding 0.127. Then we calculated the weighted mean of the five

zero-points, this corresponds to: −1.27 ± 0.08 mag (see column 3 of Table 5.2).

There is a difference of ∼ 0.2 mag between the two zero-points. In fact, if we apply our

PLKsZ relation with zero-point calibrated on Benedict et al. (2011) parallaxes to determine

the absolute magnitudes of the 71 RR Lyrae stars in our sample, we obtain a distance mod-

ulus for the LMC, determined as the weighted average of the distance moduli of these 71

RR Lyrae stars, of (m−M)0 = 18.71 ± 0.01 mag with σ = 0.09. This distance modulus

is about 0.2 mag longer than the widely adopted value of (m−M)0 = 18.5 mag.

There are a number of possible explanations for this discrepancy. First of all, we as-

sumed that all RR Lyrae stars in our sample are located at the same distance from us, equal

to the distance derived from the LMC EBs analysed by Pietrzynski et al. (2013). However,

the RR Lyrae stars could in fact be distributed along the whole depth of the LMC. Fur-

thermore, RR Lyrae stars and EBs from Pietrzynski et al. (2013) could reside in different

sub-structures of the LMC, which could be the reason for the systematic error in the deter-

mination of the zero-point. On the other hand, when calibrating the zero-point by applying

the parallaxes of the MW RR Lyrae stars by Benedict et al. (2011) we implicitly assume

that the PLKsZ relation is the same in the MW and in the LMC, which may not be true. It

is well known, in fact, that the LMC is in general more metal-poor than our Galaxy. The

difference in metal abundances could affect the PLKsZ relation of RR Lyrae stars. Indeed,

as mentioned above, the derived low metallicity dependence of our PLKsZ relation could

be due to the smaller metallicity range covered by the LMC RR Lyrae stars, that does not

reach the highest values of the Galactic variables.

We may also wonder whether there might be unknown systematic errors affecting Bene-

dict et al.’s parallaxes. These come from HST fields, which provide relative and not absolute

89

5.3. GAIA OBSERVATION OF RR LYRAE STARS IN THE MILKY WAY

trigonometric parallaxes. Absolute parallaxes of the reference stars in each field are esti-

mated via a complex procedure of fitting the spectral type and luminosity class of each star.

A general formal error of 0.5 mas is applied to the absolute parallax of the reference stars,

equal for all stars in all fields, and without justification. This could result in miscalculated

estimates of the precision of the final absolute parallax measurements of the five RR Lyrae

stars. The Lutz-Kelker bias is corrected a posteriori. In this respect it is worth of notice

that, according to van Leeuwen (2007), Hipparcos parallax of RR Lyrae itself, the only RR

Lyrae variable for which the satellite could measure the parallax with some precision (±

0.64 mas), is about 0.31 mas smaller than (Benedict et al., 2011)’s parallax for this star,

although consistent with it within the errors, hence, the corresponding distance modulus is

about 0.17 mag longer. In any case, a great contribution to the determination of the zero-

point of the RR Lyrae PLKsZ relation is expected from the ESA astrometric satellite Gaia.

We discuss this topic in Section 5.3.

We compared our new PLKsZ relation (Table 5.2) with the relations in the literature

(see Section 1.5.2). The slope in period of the RR Lyrae PLKsZ relation differs signifi-

cantly in different studies. The value derived in the present study is in excellent agreement

with that derived by Del Principe et al. (2006). Metallicities in all studies, but Sollima et al.

(2008) one, are on the Zinn & West scale, while in the current study are on a scale, which

is systematically 0.06 dex higher than the Zinn & West one. Since the difference between

two scales is small, this should not affect significantly the results of this comparison. The

dependence on metallicity of the PLKsZ relation also varies significantly among the dif-

ferent studies. Our slope in metallicity is the smallest among all previous studies and it is

closer to that found by Borissova et al. (2009).

5.3 Gaia observation of RR Lyrae stars in the Milky Way

The Gaia astrometric satellite will revolutionise many fields of astronomy (Perryman et al.,

2001). Of particular importance will be its catalogue of trigonometric parallaxes for more

than one billion stars, with astrometric precision to the µas level (see Section 1.2). Due

to Gaia’s constant observation of the sky over the five-year nominal mission, the satellite

will repeatedly observe all stars brighter than its limiting magnitude, with an average of 80

observations per star. This will also make it possible for Gaia to discover and characterise

many types of variables, including RR Lyrae stars and Cepheids.

90


Gaia is observing in the broad visual band G (Jordi et al., 2010) for its astrometric mea-

surements, and is therefore not ideal for characterising the RR Lyrae PLZ relation, which

exists only in the infrared passbands. However, since Gaia will provide accurate parallaxes

for an expected tens of thousands of MW RR Lyrae stars, it could serve as a perfect tool for

the determination of the zero-point of the PLKsZ relation through the combination with

external datasets. Moreover, Gaia will contribute significantly to the determination of the

luminosity-metallicity relation of RR Lyrae stars in the visual passband. The current largest

limiting factor in the zero-point calibration of the PLKsZ and MV − [Fe/H] relations is the

lack of a reliable and statistically significant sample of parallax measurements. The current

state of the art is the sample of five RR Lyrae parallaxes from Benedict et al. (2011) using

the HST. Gaia will improve this situation by several orders of magnitude in both precision

and numbers of objects.

In order to study the impact of Gaia in the determination of the PMKsZ and MV −

[Fe/H] relations we have selected a sample of 25 bright Galactic fundamental-mode RR

Lyrae stars with known metallicities and photometry in the Ks and V bands. We estimated

distances to the selected variables by comparing apparent and absolute magnitudes deter-

mined on the basis of the PMKsZ relation derived in this thesis work (Table 5.2) and the

MV − [Fe/H] relation (Eq. 14) in Benedict et al. (2011). Then we simulated parallaxes

along with their errors for the selected RR Lyrae stars, assuming nominal Gaia mission

performance. The simulation of Gaia parallaxes was performed by M. Palmer, using the

Gaia Object Generator (GOG; Luri et al. 2014, see Subsection 5.3.1). By using simulated

parallaxes including observational errors we recalculated the PMKsZ and MV − [Fe/H]

relations and compare them with those used for the estimate of parallaxes. This exercise

is designed to show if parallaxes determined with Gaia will allow us to derive the "true"

PMKsZ and MV − [Fe/H] relations.

Information about the 25 RRab stars in the MW, for which we simulate Gaia parallaxes,

is presented in Table 5.3. Stars listed in this table were selected because they are close and

bright enough (V<11.5 mag) to have Gaia parallaxes determined better than 2-3%. More-

over, these objects have spectroscopically derived metallicities and are the least reddened of

the nearby RR Lyrae stars. Many of them have been analysed in radial velocities and Baade-

Wesselink studies, and they do not exhibit a strong Blazko effect (Blazko, 1907). Three of

these stars are part of the sample used in this thesis work to calibrate the zero-point of the

PLKsZ relation (see Subsection 5.2.2).

91


Feast et al. (2008) derived mean Ks magnitudes of these RR Lyrae stars, by using single-

epoch Ks photometry from 2MASS (Cutri et al. 2003), ephemerides of the stars, amplitudes

in the visual passband and template fitting of the Ks light curves. Feast et al. (2008) com-

pared the derived mean Ks magnitudes with those obtained by Fernley et al. (1993), and

declare that the difference is 0.008 ± 0.0015 mag. For comparison, the average error of

the dereddened mean Ks magnitudes of our sample of 71 RR Lyrae stars in the LMC (Ta-

ble 5.1), derived by applying templates, is 0.009 mag. Since Feast et al. (2008) did not

provide the errors for the mean Ks magnitudes of the individual RR Lyrae stars in their

sample, we assumed a worse case scenario with an error of ∼ 0.01 mag and consider this

value in the determination of absolute magnitudes in the Ks passband. Feast et al. (2008)

also provided information about the reddening of the 25 RR Lyrae stars. We used these val-

ues of reddening, but since these RR Lyrae stars have small values of reddening, especially

in the Ks passband, we consider the errors in the reddening to be negligible.

We performed the transformation from the 2MASS system to the VISTA system, by

using mean Ks and J magnitudes (Feast et al., 2008) and applying the empirical relations

provided by the Cambridge Astronomy Survey Unit (CASU)1:

Ks(V ISTA) = Ks(2MASS) + 0.010 × (J −Ks)(2MASS) (5.4)

Metallicities for the 25 RR Lyrae stars, calibrated to the Zinn & West metallicity scale, were

determined spectroscopically by Layden (1994). We converted them to the metallicity scale

of our sample of 71 RR Lyrae stars by adding 0.06 dex (Gratton et al., 2004). The periods

of the RR Lyrae variables are taken from Feast et al. (2008), and coordinates are from the

SIMBAD database.

5.3.1 Simulated Gaia data

GOG (Luri et al., 2014) is designed to simulate both individual Gaia observations and the

full contents of the end-of-mission catalogue (see Section 1.2). GOG is capable of deter-

mining the expected precision in astrometric, photometric and spectroscopic observations

of Gaia. In general, the precision depends on the apparent magnitude of the star, its colour,

and its sky position, which affects the number and type of observations made (due to the

Gaia scanning law).

1http://casu.ast.cam.ac.uk/surveys-projects/vista/technical/photometric-properties

92


To obtain an absolute magnitude for each RR Lyrae star in our sample of 25 bright MW

variables, we used:

MKs = −2.70logP + 0.03[Fe/H] − 1.05 (5.5)

as determined in Table 5.2 and the zero-point fixed by the distance to the LMC. We then

obtained a distance by combining this absolute magnitude with the apparent magnitude and

extinction as defined above. Colour information as (V-I) was obtained from the Hipparcos

catalogue (Perryman and ESA, 1997) where available. The apparent magnitude, position,

colour, period, and metallicity data form the basis of a synthetic catalogue of RR Lyrae

stars, along with the distance obtained from the PMKsZ relation, and is used as the input

catalogue of ‘true’ parameters for GOG. GOG then creates simulated Gaia observations for

our sample. We take the PMKsZ relation (Eq. 5.5) as true, as a study of the possible

precision in PLKsZ calibration after the Gaia data will become available.Table 5.3 gives

the MKs magnitudes and parallaxes of the 25 MW RR Lyrae stars.

Using the fitting method described in Sect. 5.2.1 to the data including the simulated par-

allax observations and simulated errors applied to parallax, metallicity and apparent magni-

tude, we find a PMKsZ relation of:

MKs = (−2.70 ± 0.07)logP + (0.028 ± 0.008)[Fe/H]

+ (−1.01 ± 0.03) (5.6)

Comparison of these results to the input PLKsZ relation shows very good agreement.

This shows that the capabilities of fitting the absolute PLKsZ relation using Gaia parallaxes

for the 25 selected MW RR Lyrae stars will allow a precision in the zero-point of around

0.03 mag. Moreover, this is an additional test that the fitting procedure given in Sect. 5.2.1

is accurate and unbiased.

93


Star

RA

DEC

πH

ipparcos

σH

ipparcos

πGaia

σGaia

E(B

-V)

P[F

e/H

]σ[F

e/H]

Ks,VIS

TA

MK

σM

KM

VσM

V

(deg

)(d

eg)

(mas

)(m

as)

(mas

)(m

as)

(mag

)(d

ay)

(dex

)(d

ex)

(mag

)(m

ag)

(mag

)(m

ag)

(mag

)R

RLy

r29

1.36

630

42.7

8436

3.46

0.64

4.15

10.

007

0.03

00.

5668

39-1

.31

0.08

6.49

2-0

.428

0.01

10.

494

0.01

1X

Ari

47.1

2869

10.4

4590

0.88

1.32

1.96

10.

019

0.18

00.

6511

54-2

.34

0.09

7.94

5-0

.655

0.02

30.

308

0.02

7R

XEr

i72

.434

55-1

5.74

118

1.50

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5872

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8.43

2-0

.455

0.02

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502

0.01

3SW

And

5.92

954

29.4

0101

1.48

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Eri

47.9

6711

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3865

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Cet

23.0

3405

1.34

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351.

627

0.02

30.

022

0.55

3030

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128.

523

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30.

014

DX

Del

311.

8681

512

.464

080.

771.

381.

695

0.00

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092

0.47

2619

-0.5

00.

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689

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0.65

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SUD

ra17

4.48

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413

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3.12

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r23

2.75

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1.68

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571.

235

0.00

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040

0.71

4101

-1.7

60.

238.

830

-0.7

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016

0.40

80.

017

VIn

d31

7.87

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571.

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043

0.47

9604

-1.4

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118.

988

-0.2

350.

014

0.46

90.

015

XZ

Dra

287.

4275

464

.858

932.

260.

881.

361

0.00

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062

0.47

6497

-0.8

10.

099.

150

-0.2

020.

015

0.59

00.

016

BH

Peg

343.

2543

215

.787

940.

311.

821.

194

0.00

80.

077

0.64

0991

-1.3

20.

219.

070

-0.5

720.

018

0.49

80.

016

SWD

ra18

4.44

429

69.5

1062

-0.4

61.

291.

131

0.00

70.

014

0.56

9671

-1.1

80.

079.

322

-0.4

160.

016

0.51

20.

015

SVH

ya18

7.62

710

-26.

0475

44.

491.

761.

226

0.00

80.

080

0.47

8542

-1.6

40.

279.

369

-0.2

160.

018

0.42

30.

017

RUSc

l0.

7004

6-2

4.94

530

-0.1

11.

421.

275

0.00

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0.49

3347

-1.1

90.

139.

231

-0.2

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016

0.52

20.

017

AVPe

g32

8.01

164

22.5

7483

2.28

1.72

1.39

70.

006

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3903

78-0

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90.

051

0.01

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755

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XA

nd19

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0.72

2755

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0.37

20.

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RVO

ct20

6.63

230

-84.

4017

71.

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321.

057

0.00

60.

180

0.57

1169

-1.2

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259.

530

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130.

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0.50

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RS

Boo

218.

3883

931

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620.

111.

401.

298

0.00

50.

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0.37

7339

-0.2

60.

319.

509

0.07

10.

013

0.71

60.

012

WY

Ant

154.

0206

1-2

9.72

845

-0.2

41.

610.

956

0.00

60.

059

0.57

4341

-1.6

00.

209.

677

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0.42

30.

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UY

Boo

209.

6930

712

.951

791.

001.

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866

0.00

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033

0.65

0889

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30.

169.

726

-0.5

970.

018

0.27

00.

022

RYC

ol78

.782

42-4

1.62

824

1.36

1.34

1.05

30.

006

0.02

60.

4788

32-1

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0.17

9.70

5-0

.193

0.01

60.

536

0.01

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NA

qr34

9.82

168

-24.

2163

31.

822.

110.

809

0.00

80.

025

0.63

3757

-1.5

70.

159.

903

-0.5

660.

024

0.43

10.

022

AN

Ser

238.

3793

812

.961

15-1

.71

2.93

0.94

90.

007

0.04

00.

5220

690.

020.

219.

845

-0.2

830.

019

0.78

80.

018

Tabl

e5.

3:Pr

oper

tieso

f25

brig

htfu

ndam

enta

l-mod

eR

RLy

rae

star

sin

the

MW

(Col

umn

1:N

ame

ofth

est

ar;C

olum

n2:

Rig

htA

scen

sion

(J20

00)f

rom

SIM

BAD

data

base

;Col

umn

3:D

eclin

atio

n(J

2000

)fro

mSI

MBA

Dda

taba

se;C

olum

n4:

Para

llaxe

sfr

omth

ere

vise

dH

ip-

parc

osca

talo

gue

(van

Leeu

wen

,200

7);

Col

umn

5:Er

rors

ofpa

ralla

xes

from

Hip

parc

osca

talo

gue

(van

Leeu

wen

,200

7);C

olum

n6:

Gai

apa

ralla

xes

sim

ulat

edus

ing

Eq.5

.5;C

ol-

umn

7:Si

mul

ated

erro

rsof

Gai

apa

ralla

xes;

Col

umn

8:R

edde

ning

from

Feas

teta

l.(2

008)

;C

olum

n9:

Perio

dsfr

omFe

aste

tal.

(200

8);C

olum

n10

:M

etal

licity

from

Layd

en(1

994)

calib

rate

dto

the

met

allic

itysc

ale

ofth

e71

LMC

RR

Lyra

est

ars

byad

ding

0.06

dex;

Col

-um

n11

:Err

orsi

nm

etal

licity

from

Layd

en(1

994)

;Col

umn

12:K

sap

pare

ntm

agni

tude

inth

eV

ISTA

syst

em;C

olum

n13

:C

alcu

late

dab

solu

tem

agni

tude

inth

eK

spa

ssba

nd;C

ol-

umn

14:E

rror

sin

the

abso

luteK

sm

agni

tude

;Col

umn

15:C

alcu

late

dab

solu

tem

agni

tude

inth

eVJ

pass

band

;Col

umn

16:E

rror

sin

the

abso

luteVJ

mag

nitu

de).

94


5.3.2 Simulation of the MV − [Fe/H] relation of RR Lyrae stars in the MilkyWay

We applied the same approach in order to check if it will be possible to derive the MV −

[Fe/H] relation of RR Lyrae stars by using Gaia data. We used metallicities from Layden

(1994) and apparent V magnitudes from Fernley et al. (1998b). Fernley et al. (1998b) mean

V magnitudes were derived from the Hipparcos photometry and compared with mean V

magnitudes for 11 RRab and 2 RRc stars from Liu & Janes (1990). The mean difference

was found to be 0.003 mag with an rms scatter of 0.007 mag (Fernley et al., 1998b). We

assume a conservative error on the apparent mean magnitudes of ∼ 0.01 mag and consider

this value in the determination of absolute magnitudes in the V passband. We applied the

values of reddening E(B-V) from Feast et al. (2008) and determined the extinction using the

relation:

AV = 3.1E(B − V ) (5.7)

In order to obtain absolute MV magnitudes for the 25 RR Lyrae stars we applied the

relation in Benedict et al. (2011):

MV = (0.214 ± 0.047)([Fe/H] + 1.5) + (0.45 ± 0.05), (5.8)

where the metallicity is in the Zinn & West scale. Eq. 5.8 was derived using the slope

obtained by Gratton et al. (2004) and the zero-point determined from the HST parallaxes

of the five MW RR Lyrae stars measured by Benedict et al. (2011). Applying the proce-

dure described in Section 5.3.1 we simulated Gaia parallaxes and related errors of the 25

RR Lyrae stars. To fit the relation we used the method developed by M. Palmer for two

dimensions and determined a new MV − [Fe/H] relation:

MV = (0.208 ± 0.003)([Fe/H] + (0.779 ± 0.005) (5.9)

As it could be seen using Gaia parallaxes for only 25 RR Lyrae variables will allow us

to recover the slope of the relation within 3%, and to recover the zero-point to within 1%.

Obviously a larger sample of RR Lyrae stars with Gaia parallaxes will allow us to determine

the MV − [Fe/H] and PLKsZ relations with much greater precision. The main issues in

95


the future will be concerned with the accurate estimate of metallicities, mean Ks and V

magnitudes, and reddening.

96

Chapter 6

RR Lyrae stars in the VMC tile LMC8_3

6.1 Classification of EROS-2 candidate RR Lyrae stars

The EROS-2 survey provided light curves in the BEROS and REROS passbands for 16337

candidate RR Lyrae stars in the LMC, selected from EROS-2 catalogue of candidate vari-

ables on the basis of the BEROS , BEROS − REROS CMD (see left panel of Figure 2.3).

We crossmatched the EROS-2 catalogue of candidate RR Lyrae stars against the VMC cat-

alogue (internal VMC release from 5 August 2013) and found 5570 sources in common.

Among them we selected objects which are located in the tile LMC 8_3 (291 stars in total).

After discarding objects with periods longer than 4.1 days1, we obtained a sample of 268

candidate RR Lyrae stars which have a counterpart in the VMC catalogue. This sample in-

cludes also star lm0303n13977 which according to EROS-2 should have a period PEROS =

918.06335 days. However, in the OGLE III catalogue this star is listed among the RR Lyrae

stars with a period around half a day. We visually inspected the EROS-2 light curve of the

star with GRATIS and derived a new period P = 0.499556 days which in excellent agreement

with OGLE III’s. By applying Eqs. 2.1 and 2.2 we transformed the BEROS and the REROS

magnitudes to Johnson V magnitudes and analysed the light curves of the 268 candidate

RR Lyrae stars in the BEROS and V passbands with GRATIS. We corrected the period

provided by the EROS-2 survey for four stars, namely: lm0303n13977, lm0434l20435,

lm0301l25140 and lm0291l26545. Through the visual inspection of the light curves we

performed a preliminary classification of RRab, RRc, RRd stars and misclassified objects,

which light curves do not have the characteristic shape of a RR Lyrae star. According to the

1This limit in period was chosen as to include typical periods of RR Lyrae stars and their most frequentaliases.

97

6.1. CLASSIFICATION OF EROS-2 CANDIDATE RR LYRAE STARS

visual inspection of the light curves, our sample includes 252 confirmed RR Lyrae stars and

16 misclassified sources which mainly are EBs.

To classify the 268 candidate RR Lyrae stars we also plotted them on the LogP versus

AmpV diagram, (see Fig. 6.1). In this figure one can distinguish three main groups of

objects:

• LogP < −0.7 and LogP > −0.05: misclassified objects

• −0.7 ≤ LogP ≤ −0.3 and Amp(V ) ≤ 0.8 mag: RRc stars

• −0.4 ≤ LogP ≤ −0.3 and Amp(V ) > 0.8 mag or −0.3 ≤ LogP ≤ 0.05: RRab

stars

Twelve sources lie outside both the RRab and the RRc regions. All of them but one were

classified as non-RR Lyrae stars by the visual inspection of the light curves with GRATIS.

One object among these 12 stars (lm0291n13464) was classified as RRc after analysis of the

light curve. However, the star is located outside the regions of RR Lyrae stars in the period-

amplitude diagram (Figure 6.1), hence, we discarded it. Five objects (lm0434m21890,

lm0300n19430, lm0303k15709, lm0303n10802, lm0303l25724) were classified as RRab

with the period-amplitude diagram, but after the analysis with GRATIS they all were dis-

carded, since they are misclassified sources. Similarly, ten stars were classified as c-type

RR Lyrae stars with the period-amplitude diagram, but the analysis with GRATIS showed

that they are in fact RRd stars. Information about these RRd stars and the comparison with

the OGLE III catalogue, for those which were observed also by the OGLE III survey, is

presented in Table 6.1.

The final catalogue of confirmed RR Lyrae stars in tile LMC 8_3, for which EROS-2 and

VMC data are available contains 251 sources. The sample includes 167 RRab, 74 RRc and

10 RRd stars. For each star we derived mean magnitudes, amplitudes, epochs of maximum

light in the BEROS and V passbands. Some of these parameters and the classification in

type of the 251 RR Lyrae stars are presented in Table 6.2.

98


EROS-2 id P1 P0 P1/P0 OGLE III P1 OGLE III P0 OGLE III P1/P0

lm0293k.30764 0.353758 0.475592 0.7438 0.3537438 0.4755950 0.7438lm0435k.8479 0.365147 0.490433 0.7445 - - -lm0444l.8138 0.354920 0.476967 0.7441 - - -lm0293n.14230 0.362863 0.487836 0.7438 0.3629116 0.4878202 0.7440lm0310l.12653 0.362132 0.486196 0.7448 0.3621078 0.4861951 0.7448lm0303m.23391 0.385532 0.516902 0.7459 0.3855124 0.5168991 0.7458lm0303k.24363 0.391872 0.524815 0.7467 0.3918820 0.5247920 0.7467lm0301n.13911 0.357182 0.479980 0.7442 - - -lm0291n.25922 0.365509 0.490849 0.7446 - - -lm0301l.26933 0.360587 0.484494 0.7443 0.3605884 0.4844985 0.7443

Table 6.1 RRd stars in tile LMC 8_3. (Column 1: EROS-2 identification number; Column 2:First-overtone period derived with GRATIS; Column 3: Fundamental mode period derivedwith GRATIS; Column 4: Ratio of the periods; Column 5: First-overtone period from theOGLE III catalogue; Column 6: Fundamental mode period from the OGLE III catalogue ;Column 7: Ratio of the periods from the OGLE III catalogue).

Figure 6.1 Period-amplitude diagram of the 268 candidate RR Lyrae stars in tile LMC 8_3.Misclassified objects discarded from the following analysis include: short period variables(crosses) and EBs (squares).

99

6.1. CLASSIFICATION OF EROS-2 CANDIDATE RR LYRAE STARS

ERO

S-2

idR

AD

ECPe

riod

⟨BEROS⟩

Amp(B)

⟨V⟩

Amp(V)

Epoc

h(m

ax)

Type

(deg

)(d

eg)

(day

s)(m

ag)

(mag

)(m

ag)

(mag

)V

lm03

01n1

6576

77.0

3389

-66.

4998

20.

2366

4518

.75

0.21

18.8

70.

2624

5216

4.74

65c

lm03

05m

3332

76.8

9820

-66.

9698

10.

2493

1119

.51

0.36

19.6

70.

4524

5119

3.58

67c

lm03

00l1

5247

75.8

0446

-66.

5037

00.

2709

2019

.35

0.35

19.4

50.

4424

5158

9.65

12c

lm04

36l1

7456

76.2

2323

-66.

1816

90.

2773

1919

.55

0.61

19.6

00.

7124

5192

2.67

09c

lm02

93l1

8421

74.7

9358

-66.

8607

20.

2787

5919

.07

0.33

19.1

60.

3924

5229

8.65

45c

lm04

37m

2212

677

.398

74-6

6.06

973

0.28

0684

19.4

20.

4719

.52

0.58

2451

745.

8545

clm

0425

l243

8975

.464

57-6

5.86

768

0.28

1388

19.0

50.

3919

.12

0.47

2451

593.

6165

clm

0427

m19

332

75.9

2683

-66.

0407

30.

2865

4619

.11

0.36

19.1

60.

4324

5190

6.90

71c

lm04

35m

1088

877

.488

19-6

5.61

824

0.28

9555

19.1

60.

3719

.24

0.46

2451

927.

6789

clm

0425

l205

1375

.501

09-6

5.84

096

0.28

9973

18.8

20.

4718

.87

0.59

2450

508.

6286

clm

0423

l200

6975

.597

47-6

5.49

339

0.29

1086

19.0

80.

5119

.13

0.60

2451

467.

6728

clm

0302

n485

876

.137

49-6

6.78

444

0.29

2002

19.0

00.

4519

.05

0.56

2451

493.

6596

clm

0291

k248

6275

.000

92-6

6.40

342

0.29

3334

19.6

80.

4220

.02

0.56

2451

128.

6539

clm

0435

m91

0977

.321

64-6

5.60

798

0.29

5152

18.9

20.

4819

.02

0.56

2450

706.

7920

clm

0434

n143

1076

.706

55-6

5.80

327

0.29

6573

19.2

00.

4019

.28

0.52

2451

905.

5749

clm

0291

l119

4074

.899

17-6

6.47

166

0.30

3318

19.2

00.

4819

.31

0.57

2451

886.

5948

clm

0424

m19

442

75.1

0627

-65.

6782

00.

3046

0519

.29

0.44

19.4

10.

6124

5118

2.68

72c

lm04

25n1

5519

75.7

8383

-65.

8018

40.

3075

0719

.00

0.43

19.0

80.

4824

5183

0.71

42c

lm02

91n2

5551

75.1

1817

-66.

5556

60.

3083

2218

.90

0.45

19.0

30.

5324

5188

5.60

54c

lm04

25n1

8680

75.9

2700

-65.

8217

30.

3103

6619

.24

0.54

19.2

70.

7124

5159

1.62

72c

lm03

04m

2952

75.9

4720

-66.

9718

50.

3119

4419

.08

0.41

19.2

10.

5224

5120

7.61

61c

lm03

03n3

1583

77.1

4986

-66.

9305

00.

3141

8019

.15

0.45

19.1

90.

5324

5230

7.63

81c

lm03

01n7

929

76.8

9016

-66.

4461

00.

3142

7119

.14

0.47

19.2

40.

5524

5087

1.57

79c

lm04

25k9

319

75.4

7239

-65.

6096

70.

3196

9719

.55

0.55

19.7

50.

6924

5147

8.61

92c

lm04

34l2

3190

76.2

3528

-65.

8782

70.

3225

9519

.27

0.46

19.3

30.

5124

5202

0.51

10c

lm03

03m

2250

477

.154

98-6

6.72

917

0.32

3404

19.4

50.

4419

.46

0.51

2452

204.

7726

clm

0425

n137

5375

.738

00-6

5.79

020

0.32

4285

19.5

10.

4619

.56

0.59

2451

125.

6205

clm

0303

n168

4177

.102

76-6

6.84

558

0.32

7493

19.2

30.

3819

.33

0.46

2451

078.

7631

clm

0291

n154

1275

.414

71-6

6.49

017

0.32

8223

19.3

10.

4119

.46

0.50

2451

124.

7292

clm

0300

m68

0876

.005

54-6

6.28

864

0.32

9139

19.1

80.

3719

.26

0.46

2451

491.

6430

c

100

CHAPTER 6. RR LYRAE STARS IN THE VMC TILE LMC 8_3lm

0301

m15

847

77.1

2213

-66.

3411

20.

3300

7719

.11

0.54

19.2

10.

6424

5119

9.56

39c

lm04

36m

8308

76.7

2609

-65.

9659

90.

3316

1919

.11

0.45

19.3

90.

5424

5177

4.83

16c

lm03

12l1

5193

77.4

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6.1. CLASSIFICATION OF EROS-2 CANDIDATE RR LYRAE STARSlm

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.858

77-6

6.97

363

0.71

0488

19.0

30.

6519

.19

0.75

2451

533.

6272

ablm

0305

m78

5077

.223

90-6

6.99

474

0.71

3324

18.7

60.

2718

.88

0.32

2451

502.

6255

ablm

0427

m63

3875

.990

25-6

5.94

538

0.71

3501

19.1

60.

6319

.28

0.71

2452

395.

4980

ablm

0434

n173

8376

.513

44-6

5.89

259

0.72

4152

18.8

30.

3119

.04

0.39

2452

254.

5884

ablm

0301

l164

8776

.556

35-6

6.50

519

0.73

8143

18.9

80.

1819

.24

0.22

2452

008.

5249

ablm

0300

l234

6275

.602

95-6

6.58

330

0.74

4314

18.7

60.

5518

.97

0.64

2451

886.

6168

ablm

0310

l189

1177

.523

38-6

6.53

928

0.74

8431

19.0

40.

3819

.29

0.45

2452

213.

7774

abTa

ble

6.2:

Prop

ertie

sof

the

251

confi

rmed

RR

Lyra

est

ars

intil

eLM

C8_

3(C

olum

n1:

ERO

S-2

iden

tifica

tion

ofth

est

ar;C

olum

n2:

Rig

htas

-ce

nsio

nfr

omth

eER

OS-

2ca

talo

gue;

Col

umn

3:D

eclin

atio

nfr

omth

eER

OS-

2ca

talo

gue;

Col

umn

4:Pe

riod

from

the

ERO

S-2

cata

logu

e(a

-St

ars

for

whi

cha

new

perio

dw

ases

timat

edin

this

stud

y);

Col

umn

5:M

ean

mag

nitu

dein

theB

EROS

band

;C

olum

n6:

Am

plitu

dein

the

BEROS

band

;C

olum

n7:

Mea

nm

agni

tude

inth

eV

band

;C

olum

n8:

Am

plitu

dein

theV

band

;Col

umn

9:Ep

och

ofm

axim

umlig

htin

theV

band

;Col

umn

10:C

lass

ifica

tion

inty

pe).

107

6.2. COMPARISON WITH THE OGLE III CATALOGUE

6.2 Comparison with the OGLE III catalogue

We compared our classification of the RR Lyrae stars in tile LMC 8_3 with the classifica-

tion provided in the OGLE III catalogue. The OGLE III survey covered only part of the

tile LMC 8_3. We were able to make a comparison for 72 RR Lyrae stars which are in

common between the two catalogues. Information about these 72 objects is presented in

Table 6.3. For the majority of the RR Lyrae stars our classification is in agreement with the

classification provided by OGLE III, but there are some discrepancies.

According to the OGLE III classification the source lm0305m3332 is an RRab star, but

we classified it as RRc star. Also the period of this star, determined by the EROS-2 survey

(P=0.249311 day), differs from the period provided by the OGLE III survey (P=0.4986339

day). After analysis of the light curve with GRATIS we concluded that OGLE III provided

an alias of the actual period. Star lm0293l18421 was classified as RRc by us and as RRe by

the OGLE III. Star lm0300l14647 is an RRd star according to the OGLE III classification,

but we analysed the light curve with GRATIS and did not confirm the existence of a second

periodicity, therefore, we classified the star as c-type RR Lyrae. Star lm0293n31080 is

RRab in the OGLE III classification and RRc in our classification.

108


OG

LEII

Iid

ERO

S-2

idR

AD

ECTy

peI

VP

Epoc

h(m

ax)

(HH

:MM

:SS)

(DD

:MM

:SS)

(mag

)(m

ag)

(day

)(H

JD-2

4500

00)

OG

LE-L

MC

-RR

LYR

-024

65lm

0292

n226

124:

58:0

2.47

-66:

53:5

8.2

RR

ab18

.836

19.4

110.

6240

672

2166

.648

31O

GLE

-LM

C-R

RLY

R-0

2630

lm02

93k2

8352

4:58

:53.

66-6

6:45

:52.

4R

Rab

18.7

5219

.215

0.49

7780

021

66.8

0015

OG

LE-L

MC

-RR

LYR

-027

40lm

0293

l184

214:

59:1

0.51

-66:

51:3

9.0

RR

e18

.778

19.1

430.

2787

614

2166

.797

15O

GLE

-LM

C-R

RLY

R-0

2767

lm02

93l1

2631

4:59

:13.

54-6

6:49

:39.

4R

Rab

18.7

5019

.396

0.61

0866

021

66.7

2786

OG

LE-L

MC

-RR

LYR

-027

95lm

0293

l255

064:

59:1

8.97

-66:

54:0

6.6

RR

ab18

.582

19.1

810.

6579

816

2166

.798

64O

GLE

-LM

C-R

RLY

R-0

2814

lm02

93k3

928

4:59

:23.

82-6

6:37

:16.

8R

Rab

18.8

1119

.292

0.47

1742

321

72.5

6258

OG

LE-L

MC

-RR

LYR

-028

41lm

0293

k252

264:

59:3

0.49

-66:

44:4

4.4

RR

ab18

.707

19.2

900.

5864

819

2166

.593

34O

GLE

-LM

C-R

RLY

R-0

2913

lm02

93k3

0764

4:59

:48.

97-6

6:46

:36.

5R

Rd

19.1

2319

.625

0.35

3743

821

66.5

8727

OG

LE-L

MC

-RR

LYR

-029

28lm

0293

l525

24:

59:5

1.57

-66:

47:0

1.2

RR

ab18

.826

19.4

490.

6129

133

2166

.368

64O

GLE

-LM

C-R

RLY

R-0

3045

lm02

93m

1098

85:

00:1

8.38

-66:

39:4

0.5

RR

c18

.852

19.3

550.

3661

132

2166

.545

33O

GLE

-LM

C-R

RLY

R-0

3129

lm02

93n3

1080

5:00

:37.

50-6

6:55

:55.

6R

Rab

19.1

8419

.610

0.43

6512

321

66.7

3257

OG

LE-L

MC

-RR

LYR

-031

44lm

0293

n182

295:

00:4

0.54

-66:

51:2

8.8

RR

ab18

.718

19.3

220.

6281

261

2166

.469

07O

GLE

-LM

C-R

RLY

R-0

3159

lm02

93m

1700

05:

00:4

4.55

-66:

41:4

5.6

RR

ab18

.754

19.3

420.

5952

245

2166

.303

04O

GLE

-LM

C-R

RLY

R-0

3174

lm02

93m

1437

55:

00:4

8.01

-66:

40:5

0.0

RR

ab18

.712

19.2

120.

5079

962

2166

.587

39O

GLE

-LM

C-R

RLY

R-0

3227

lm02

93m

1900

35:

01:0

2.85

-66:

42:2

6.3

RR

ab18

.853

19.4

490.

5835

871

2166

.304

63O

GLE

-LM

C-R

RLY

R-0

3255

lm02

93m

1962

85:

01:0

9.79

-66:

42:3

9.7

RR

ab18

.681

19.2

440.

5811

319

2166

.723

46O

GLE

-LM

C-R

RLY

R-0

3330

lm02

93n2

0870

5:01

:26.

59-6

6:52

:17.

4R

Rab

18.5

7319

.099

0.57

8191

421

66.6

3326

OG

LE-L

MC

-RR

LYR

-033

82lm

0293

m19

803

5:01

:38.

65-6

6:42

:39.

2R

Rc

18.9

3819

.371

0.33

8544

921

66.7

3510

OG

LE-L

MC

-RR

LYR

-034

23lm

0293

n142

305:

01:4

8.55

-66:

49:5

4.7

RR

d18

.774

19.2

280.

3629

116

2166

.607

85O

GLE

-LM

C-R

RLY

R-0

3425

lm02

93n3

0795

5:01

:48.

98-6

6:55

:40.

0R

Rab

18.8

2119

.338

0.47

4009

821

66.6

9079

OG

LE-L

MC

-RR

LYR

-035

24lm

0300

l146

475:

02:1

1.22

-66:

35:3

4.9

RR

d18

.543

19.0

470.

4336

058

2166

.577

04O

GLE

-LM

C-R

RLY

R-0

3580

lm03

00l2

3462

5:02

:24.

69-6

6:35

:00.

3R

Rab

18.4

1218

.995

0.74

4310

121

66.4

9600

OG

LE-L

MC

-RR

LYR

-036

02lm

0302

k147

965:

02:2

9.31

-66:

44:2

9.6

RR

ab18

.831

19.4

100.

5596

368

2166

.543

48O

GLE

-LM

C-R

RLY

R-0

3637

lm03

02l1

6395

5:02

:38.

91-6

6:51

:46.

4R

Rc

18.8

3819

.278

0.34

4596

321

66.5

3368

OG

LE-L

MC

-RR

LYR

-036

54lm

0300

l255

665:

02:4

1.69

-66:

34:4

7.2

RR

ab18

.716

19.2

830.

6381

508

2172

.629

08O

GLE

-LM

C-R

RLY

R-0

3689

lm03

02l2

6417

5:02

:49.

15-6

6:55

:50.

3R

Rab

19.0

3619

.687

0.59

0301

821

66.7

5562

OG

LE-L

MC

-RR

LYR

-037

17lm

0302

l129

605:

02:5

5.86

-66:

50:2

2.4

RR

ab18

.646

19.1

960.

5673

193

2166

.529

92O

GLE

-LM

C-R

RLY

R-0

3722

lm03

02k3

782

5:02

:57.

11-6

6:37

:52.

8R

Rc

18.9

4119

.431

0.35

2435

321

66.8

2662

OG

LE-L

MC

-RR

LYR

-037

49lm

0302

k502

25:

03:0

1.62

-66:

38:3

3.1

RR

c18

.843

19.3

560.

4042

293

2166

.551

34O

GLE

-LM

C-R

RLY

R-0

3757

lm03

00l1

3312

5:03

:02.

53-6

6:35

:40.

6R

Rab

18.7

3019

.244

0.52

7450

621

66.5

5412

109

6.2. COMPARISON WITH THE OGLE III CATALOGUEO

GLE

-LM

C-R

RLY

R-0

3858

lm03

02l1

2678

5:03

:25.

28-6

6:50

:15.

2R

Rab

19.0

4019

.470

0.42

4944

821

66.5

2539

OG

LE-L

MC

-RR

LYR

-038

81lm

0302

l232

975:

03:3

0.11

-66:

54:2

9.5

RR

ab18

.909

19.4

910.

5114

616

2166

.332

40O

GLE

-LM

C-R

RLY

R-0

3902

lm03

02k1

3534

5:03

:36.

12-6

6:43

:54.

3R

Rab

18.6

2219

.256

0.62

0880

921

66.2

5905

OG

LE-L

MC

-RR

LYR

-039

56lm

0302

n123

515:

03:4

5.85

-66:

49:5

5.3

RR

ab19

.107

19.7

970.

5661

573

2166

.290

86O

GLE

-LM

C-R

RLY

R-0

3960

lm03

00n2

7286

5:03

:46.

69-6

6:34

:50.

3R

Rab

18.6

4919

.185

0.56

6303

321

66.6

4361

OG

LE-L

MC

-RR

LYR

-039

65lm

0304

m29

525:

03:4

7.34

-66:

58:1

8.9

RR

c18

.835

19.2

210.

3119

118

2166

.721

70O

GLE

-LM

C-R

RLY

R-0

4196

lm03

02n4

858

5:04

:33.

01-6

6:47

:04.

3R

Rc

18.8

5719

.200

0.29

2003

821

66.7

3196

OG

LE-L

MC

-RR

LYR

-042

99lm

0302

n235

235:

04:5

0.69

-66:

53:5

9.9

RR

ab18

.710

19.1

310.

4971

214

2166

.768

38O

GLE

-LM

C-R

RLY

R-0

4522

lm03

02m

2248

75:

05:1

4.23

-66:

45:4

8.0

RR

ab19

.106

19.6

420.

5204

521

2166

.599

96O

GLE

-LM

C-R

RLY

R-0

4643

lm03

01l2

6933

5:05

:33.

87-6

6:34

:44.

9R

Rd

18.7

02-9

9.99

00.

3605

884

2166

.804

71O

GLE

-LM

C-R

RLY

R-0

4736

lm03

03l2

6148

5:05

:49.

03-6

6:54

:14.

3R

Rab

18.6

4219

.235

0.62

0648

421

66.7

0892

OG

LE-L

MC

-RR

LYR

-048

53lm

0305

k570

45:

06:0

9.35

-66:

59:1

5.3

RR

ab18

.861

19.5

200.

6215

964

2166

.416

11O

GLE

-LM

C-R

RLY

R-0

4942

lm03

03l2

7610

5:06

:22.

59-6

6:54

:42.

0R

Rab

18.6

1019

.211

0.62

3747

921

66.5

6503

OG

LE-L

MC

-RR

LYR

-050

88lm

0303

l865

55:

06:4

6.46

-66:

48:0

2.7

RR

c18

.608

18.9

800.

3391

250

2166

.605

45O

GLE

-LM

C-R

RLY

R-0

5094

lm03

03k2

5210

5:06

:48.

56-6

6:44

:45.

7R

Rab

18.9

5419

.530

0.52

4921

021

66.7

6883

OG

LE-L

MC

-RR

LYR

-051

43lm

0303

k243

635:

06:5

5.56

-66:

44:2

7.3

RR

d18

.507

18.9

820.

3918

820

2166

.542

81O

GLE

-LM

C-R

RLY

R-0

5144

lm03

03l1

7671

5:06

:55.

64-6

6:51

:12.

7R

Rab

18.6

6319

.150

0.56

0584

921

66.5

6231

OG

LE-L

MC

-RR

LYR

-052

38lm

0303

m23

391

5:07

:13.

26-6

6:44

:14.

2R

Rd

18.8

7719

.533

0.38

5512

421

66.7

4170

OG

LE-L

MC

-RR

LYR

-052

63lm

0303

n153

225:

07:1

7.67

-66:

50:2

0.1

RR

ab18

.844

19.3

690.

5057

311

2166

.552

55O

GLE

-LM

C-R

RLY

R-0

5317

lm03

05m

3882

5:07

:26.

13-6

6:58

:25.

3R

Rab

18.6

2919

.242

0.71

0487

521

66.6

6993

OG

LE-L

MC

-RR

LYR

-053

60lm

0303

n161

025:

07:3

3.62

-66:

50:3

5.1

RR

ab18

.609

19.1

210.

6324

295

2166

.329

94O

GLE

-LM

C-R

RLY

R-0

5375

lm03

05m

3332

5:07

:35.

60-6

6:58

:11.

5R

Rab

19.1

7719

.677

0.49

8633

921

66.8

7261

OG

LE-L

MC

-RR

LYR

-054

05lm

0303

n127

995:

07:3

9.77

-66:

49:2

3.6

RR

ab18

.816

19.4

230.

5818

589

2166

.637

84O

GLE

-LM

C-R

RLY

R-0

5426

lm03

03n1

3977

5:07

:44.

26-6

6:49

:48.

9R

Rab

18.9

7819

.472

0.49

9565

521

66.5

0195

OG

LE-L

MC

-RR

LYR

-054

46lm

0303

m10

773

5:07

:47.

87-6

6:39

:37.

1R

Rc

18.7

4019

.213

0.34

4941

421

66.7

8490

OG

LE-L

MC

-RR

LYR

-054

76lm

0305

m62

945:

07:5

3.60

-66:

59:1

5.2

RR

c18

.650

19.0

950.

3666

785

2166

.876

90O

GLE

-LM

C-R

RLY

R-0

5490

lm03

03m

1715

25:

07:5

6.06

-66:

41:5

5.2

RR

ab18

.735

19.2

400.

5242

037

2166

.412

07O

GLE

-LM

C-R

RLY

R-0

5539

lm03

03m

2124

55:

08:0

3.26

-66:

43:2

3.3

RR

ab18

.659

19.2

370.

5935

504

2166

.768

82O

GLE

-LM

C-R

RLY

R-0

5551

lm03

03n9

745

5:08

:04.

51-6

6:48

:15.

8R

Rab

18.8

2419

.455

0.62

8778

721

66.3

2230

OG

LE-L

MC

-RR

LYR

-055

76lm

0303

m22

989

5:08

:07.

85-6

6:43

:59.

3R

Rc

18.4

3518

.937

0.42

7377

821

66.6

7659

OG

LE-L

MC

-RR

LYR

-056

17lm

0303

m17

812

5:08

:16.

34-6

6:42

:07.

3R

Rab

18.8

0319

.414

0.56

5554

521

66.6

4750

OG

LE-L

MC

-RR

LYR

-056

72lm

0303

n168

415:

08:2

4.70

-66:

50:4

4.4

RR

c19

.013

19.5

200.

3274

989

2166

.704

72O

GLE

-LM

C-R

RLY

R-0

5721

lm03

03m

5651

5:08

:33.

42-6

6:37

:37.

5R

Rab

18.7

0219

.331

0.69

2535

521

66.3

3100

110

CHAPTER 6. RR LYRAE STARS IN THE VMC TILE LMC 8_3O

GLE

-LM

C-R

RLY

R-0

5732

lm03

03m

1100

55:

08:3

5.84

-66:

39:3

5.7

RR

ab18

.641

19.2

520.

6437

728

2166

.677

16O

GLE

-LM

C-R

RLY

R-0

5734

lm03

03n3

1583

5:08

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01-6

6:55

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0R

Rc

18.9

7519

.395

0.31

4178

321

66.8

7421

OG

LE-L

MC

-RR

LYR

-057

40lm

0303

m22

504

5:08

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25-6

6:43

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Rc

19.0

77-9

9.99

00.

3234

019

2223

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GLE

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C-R

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R-0

5815

lm03

03n2

7302

5:08

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Rab

18.8

7819

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0.58

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921

66.8

5939

OG

LE-L

MC

-RR

LYR

-058

42lm

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m78

505:

08:5

3.76

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59:4

1.2

RR

ab18

.620

19.2

860.

7133

254

2166

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GLE

-LM

C-R

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R-0

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lm03

12k4

503

5:09

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40-6

6:37

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Rab

18.8

4119

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0.61

3850

321

66.6

6862

OG

LE-L

MC

-RR

LYR

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13lm

0312

k211

115:

09:3

4.39

-66:

46:1

2.1

RR

ab18

.920

19.3

550.

4605

988

2166

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GLE

-LM

C-R

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R-0

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12l1

5193

5:09

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24-6

6:51

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1R

Rc

19.0

4819

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0.33

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321

66.8

3342

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LE-L

MC

-RR

LYR

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73lm

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535:

09:4

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35:3

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d18

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19.4

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ble

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star

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from

the

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IIIc

atal

ogue

).

111

6.3. FOURIER ANALYSIS OF THE RR LYRAE STARS IN TILE LMC 8_3

6.3 Fourier analysis of the RR Lyrae stars in tile LMC 8_3

The Fourier decomposition of the light curves was also used to check the classification of

the RR Lyrae stars in tile LMC 8_3 and to infer their metallicity (see Section 1.5.1). In order

to perform the Fourier analysis we first transformed the light curves in the EROS passbands

to the V -band using Eqs. 2.1 and 2.2, and then cleaned the V -band light curves of the 251

confirmed RR Lyrae stars from the possible outliers, according to the following iterative

procedure:

• we discarded all data-points with residuals > 0.200 mag from GRATIS best fit model

of the light curve;

• we checked the standard deviation σ of the distribution of residuals:

– if σ < 0.070 mag we stopped the cleaning procedure;

– if σ > 0.070 mag we discarded also data points with residual ∈ (0.150, 0.200)

mag from the best fit model.

• we again checked the standard deviation σ of the distribution of residuals:

– if σ < 0.070 mag we stopped the cleaning procedure;

– if σ > 0.070 mag we discarded also data points with residual ∈ (0.100, 0.150)

mag from the best fit model.

Note that all light curves still have more than 73 data points after this cleaning proce-

dure. We performed the sine Fourier decomposition of the light curves and derived normal-

ized Fourier parameters A21, A31, φ21, φ31 and the Dm values (see Section 1.5.1). Some of

these parameters are listed in Table 6.4.

Figure 6.2 shows the distribution of the 251 RR Lyrae stars in our sample on the A21

versus φ21 plane. The vast majority of the RR Lyrae stars are located in two well separated

regions which correspond to the RRab (upper-left region) and RRc (bottom-right region)

stars. Thus, the Fourier analysis generally confirms our classification based on the visual

inspection of the light curves and the period-amplitude diagram. A few deviating objects

in Figure 6.2 deserve further discussion. Star lm0427l17346 lies rather separated from

both groups. We visually inspected its light curve and analysed its position on the period-

amplitude diagram (Fig. 6.1), but did not find any peculiarities. Stars lm0293n31080 and

112


Figure 6.2 A21 Fourier parameter versus φ21. Empty circles are RRab stars, filled circlesare RRc variables. Errors are omitted for clarifying, but they are provided in Table 6.4.

lm0434l7912 were classified as RRc, however they are both located in the region of the

fundamental-mode RR Lyrae stars in Figure 6.2. It should be noted that one of them (star

lm0293n31080) was classified as RRab also by the OGLE III survey. On the contrary, star

lm0426n9666, which we classified as RRab, is located in the region of the first-overtone

mode RR Lyrae stars. In the following, for these few objects we adopted the classification

based on the visual inspection of the light curves and the period-amplitude diagram.

Figure 6.3 shows the distribution of RR Lyrae stars on the φ31 versus logarithm of period

plane. There is a clear separation between RRab and RRc stars. Furthermore, for the RRab

stars there is a quite clear linear correlation of the φ31 parameter with Log(P), whereas the

correlation is definitely worse and errors are much larger for the RRc stars.

113

6.3. FOURIER ANALYSIS OF THE RR LYRAE STARS IN TILE LMC 8_3

Figure 6.3 φ31 parameter versus logarithm of the period. Empty circles are RRab stars,filled circles are RRc stars.

114


ERO

S-2

idTy

peφ21

σφ21

φ31

σφ31

A21

σA

21

A31

σA

31

Dm

lm03

01n1

6576

c2.

582

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87.

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497

0.08

10.

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067

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lm03

05m

3332

c2.

929

0.13

75.

286

0.46

30.

222

0.02

90.

070.

026

12.2

4lm

0300

l152

47c

2.97

40.

821

7.33

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954

0.03

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020.

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0.01

877

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lm04

36l1

7456

c2.

780.

182

4.56

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467

0.13

0.02

30.

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3.28

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7lm

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085.

482

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111

5.88

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099

4.33

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3.06

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k931

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3.15

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14.4

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l231

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2.67

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7.46

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0.12

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0.01

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lm03

03m

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2.89

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0.10

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6.07

lm04

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3753

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0.20

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111

0.02

35.2

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n168

41c

3.1

0.20

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0.74

40.

103

0.02

0.03

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64.1

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0291

n154

12c

3.09

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30.

566

0.11

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020.

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0.01

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lm03

00m

6808

c2.

557

0.11

76.

998

0.27

40.

157

0.01

80.

063

0.01

815

.81

115

6.3. FOURIER ANALYSIS OF THE RR LYRAE STARS IN TILE LMC 8_3lm

0301

m15

847

c2.

893

0.07

45.

838

0.20

60.

241

0.01

70.

088

0.01

612

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lm04

36m

8308

c3.

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1.47

76.

572

0.64

60.

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0.01

30.

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0.01

817

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lm03

12l1

5193

c2.

536

0.11

25.

699

0.22

40.

206

0.02

20.

104

0.02

18.

3lm

0425

k462

5c

3.44

20.

417.

988

0.57

60.

088

0.02

80.

055

0.02

671

.25

lm04

23l1

7670

c3.

157

0.14

36.

20.

656

0.14

10.

020.

037

0.01

89.

7lm

0293

m19

803

c2.

782

0.13

26.

773

0.94

30.

136

0.01

80.

022

0.01

558

.37

lm03

03l8

655

c3.

60.

238

2.64

11.

271

0.13

80.

031

0.02

30.

023

39.7

1lm

0310

n115

85c

3.50

60.

157

5.97

80.

666

0.23

60.

036

0.06

70.

0310

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lm03

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753

c3.

104

0.15

56.

582

0.53

50.

143

0.02

20.

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0.02

9.62

lm04

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c2.

905

0.51

27.

136

1.39

0.06

90.

028

0.01

70.

021

24.5

3lm

0302

l163

95c

3.60

70.

253

7.46

30.

558

0.11

80.

028

0.05

60.

026

63.4

9lm

0303

m10

773

c3.

372

0.13

66.

777

0.42

0.13

60.

018

0.04

90.

017

12.4

5lm

0425

l648

1c

3.11

30.

169

6.16

30.

281

0.13

60.

022

0.07

70.

022

9.2

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35m

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4.27

40.

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7.67

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0.04

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21.7

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1.04

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0.01

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c3.

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0.19

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560.

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0.13

60.

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0.04

50.

023

49.2

3lm

0300

l889

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2.55

40.

146

5.67

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0.11

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0.11

20.

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12.2

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c2.

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0.17

96.

243

0.62

60.

115

0.02

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018

25.6

5lm

0436

n142

85c

2.22

70.

154

4.76

50.

802

0.16

40.

024

0.03

70.

029.

08lm

0302

k378

2c

2.54

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251

7.29

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576

0.15

0.03

50.

067

0.03

155

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lm04

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188

0.34

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239

0.37

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0.02

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0.02

239

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d2.

961

0.14

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0.51

20.

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0.02

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0.02

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350.

544

0.15

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0.05

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17.3

1lm

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m13

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c3.

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0.17

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0.91

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0.02

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0.02

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3.31

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503

4.55

11.

199

0.08

10.

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0.02

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44.4

7lm

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k107

85c

2.69

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175

6.27

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0.12

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0.07

50.

0214

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2.62

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7.27

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397

0.15

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0.09

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72.2

9lm

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l269

33d

3.39

30.

203

6.64

60.

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0.13

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27.7

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2.87

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6.04

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0.02

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3.99

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116


0435

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0.15

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0.29

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0.07

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32.7

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0.02

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14.5

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3.00

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6.55

50.

216

0.17

20.

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0.08

30.

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27.4

7lm

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k930

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3.33

70.

108

5.30

20.

332

0.15

60.

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0.05

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18.1

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m22

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c2.

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0.16

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653

1.15

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0.02

30.

020.

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22.4

8lm

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2.94

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17.

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0.66

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0.02

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0.02

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34.3

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l198

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2.84

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6.94

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0.09

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0.01

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12.6

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4.99

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5.15

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0.12

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0.07

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3.30

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5.65

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0.20

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9.5

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2.19

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850.

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4.59

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0.31

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2.41

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7.35

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0.01

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106

0.02

147

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lm04

36n1

1172

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136

0.03

14.

731

0.04

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0.01

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333

0.01

41.

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0300

l146

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3.45

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112

5.65

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249

0.24

60.

027

0.11

50.

024

10.8

1lm

0293

n310

80c

2.12

50.

062

4.33

10.

170.

335

0.01

90.

119

0.01

823

.27

lm04

34l7

912

c2.

195

0.08

44.

043

0.26

40.

446

0.03

40.

131

0.02

937

.59

lm03

12k2

1111

ab2.

101

0.03

24.

626

0.04

30.

506

0.01

40.

325

0.01

42.

16lm

0293

k392

8ab

2.07

30.

035

4.51

40.

058

0.41

50.

013

0.23

40.

012

9.58

lm02

93n3

0795

ab2.

222

0.03

64.

769

0.05

20.

50.

016

0.30

80.

016

2.31

lm04

32l1

2420

ab2.

122

0.08

34.

650.

390.

284

0.02

20.

063

0.01

942

.88

lm04

27n7

741

ab2.

256

0.02

64.

699

0.03

60.

474

0.01

10.

305

0.01

11.

2lm

0300

m99

35ab

2.29

70.

039

4.61

0.05

30.

397

0.01

40.

264

0.01

49.

15lm

0437

k157

72ab

2.23

30.

031

4.65

40.

043

0.49

50.

014

0.31

70.

014

1.88

lm04

34l2

0435

ab2.

171

0.03

44.

754

0.04

60.

491

0.01

50.

318

0.01

51.

49lm

0437

k226

54ab

2.27

50.

036

4.76

40.

053

0.51

0.01

70.

308

0.01

62.

39

117


0436

n206

28ab

2.21

30.

041

4.47

30.

055

0.43

20.

016

0.28

90.

016

4.37

lm03

02n2

3523

ab2.

340.

043

4.55

0.06

90.

367

0.01

40.

211

0.01

410

.81

lm02

93k2

8352

ab2.

254

0.03

34.

534

0.04

20.

404

0.01

20.

291

0.01

26.

65lm

0303

n139

77ab

2.25

40.

031

4.52

40.

042

0.44

90.

013

0.30

10.

013

1.53

lm03

03n1

5322

ab2.

162

0.03

24.

710.

044

0.48

90.

014

0.31

50.

014

1.76

lm02

93m

1437

5ab

2.18

90.

029

4.67

80.

040.

510.

014

0.32

80.

013

2.55

lm03

01l2

4255

ab2.

201

0.03

44.

732

0.04

70.

510.

016

0.32

50.

015

2.32

lm04

36l2

0450

ab2.

246

0.04

34.

792

0.05

90.

564

0.02

20.

366

0.02

13.

12lm

0437

m20

444

ab2.

439

0.03

65.

141

0.05

70.

553

0.01

80.

312

0.01

62.

07lm

0302

l232

97ab

2.13

40.

036

4.67

60.

050.

547

0.01

70.

341

0.01

73.

26lm

0291

m87

10ab

2.29

40.

045

4.84

90.

073

0.43

40.

018

0.23

90.

017

1.8

lm04

35k2

0062

ab2.

142

0.03

94.

654

0.05

30.

511

0.01

80.

332

0.01

82.

55lm

0291

n201

01ab

2.30

20.

028

4.81

40.

039

0.46

70.

012

0.30

30.

012

1.67

lm03

00m

1717

8ab

2.25

90.

035

4.76

50.

048

0.51

90.

016

0.33

90.

016

2.19

lm03

02m

2248

7ab

2.44

30.

052

4.68

90.

060.

357

0.01

80.

297

0.01

86.

57lm

0303

m17

152

ab2.

312

0.03

94.

844

0.05

60.

535

0.01

90.

332

0.01

82.

93lm

0300

k121

84ab

2.29

40.

038

4.76

0.05

60.

396

0.01

40.

245

0.01

41.

69lm

0303

k252

10ab

2.59

60.

045

5.56

60.

073

0.51

60.

021

0.27

60.

019

0.87

lm04

35m

1779

3ab

2.23

50.

034

4.74

40.

048

0.47

30.

015

0.29

80.

014

1.3

lm04

35m

2356

3ab

2.38

30.

047

4.86

70.

091

0.35

90.

016

0.17

50.

015

4.13

lm04

25n2

3250

ab2.

093

0.04

54.

581

0.07

50.

468

0.01

90.

258

0.01

82.

73lm

0300

m19

324

ab2.

410.

033

4.87

10.

058

0.36

70.

011

0.19

30.

011

3.92

lm03

00l1

3312

ab2.

174

0.03

94.

439

0.05

60.

453

0.01

60.

281

0.01

62.

59lm

0291

n604

0ab

2.32

40.

034

4.67

70.

048

0.40

80.

013

0.26

60.

013

2.65

lm03

01n1

6814

ab2.

245

0.03

44.

629

0.06

40.

439

0.01

40.

210.

013

6.98

lm04

26n1

2018

ab2.

096

0.05

34.

590.

073

0.45

80.

022

0.29

70.

022

1.86

lm02

91n2

0061

ab2.

207

0.04

24.

582

0.07

0.39

90.

015

0.22

20.

015

6.67

lm03

01n2

1605

ab2.

063

0.03

34.

703

0.04

0.43

30.

013

0.33

70.

013

5.24

lm03

01m

2278

0ab

2.26

70.

037

4.75

90.

050.

495

0.01

60.

325

0.01

61.

26lm

0301

k175

54ab

2.29

90.

041

4.96

70.

060.

510.

019

0.30

40.

018

1.58

lm04

25l1

4852

ab2.

126

0.03

24.

753

0.04

40.

515

0.01

50.

325

0.01

52.

29lm

0437

m17

477

ab2.

062

0.05

94.

552

0.09

10.

336

0.01

80.

213

0.01

719

.77

lm03

10k1

1253

ab2.

233

0.04

54.

797

0.06

30.

515

0.02

10.

331

0.02

2.19

118


0434

k220

95ab

2.28

30.

034

4.94

50.

050.

535

0.01

60.

327

0.01

62.

1lm

0425

k115

00ab

2.15

40.

064

4.44

10.

086

0.34

20.

020.

245

0.02

3.99

lm04

34m

6139

ab2.

156

0.03

74.

728

0.04

90.

528

0.01

70.

348

0.01

72.

26lm

0301

m15

584

ab2.

317

0.03

5.08

80.

043

0.53

90.

015

0.33

10.

014

1.67

lm04

46k2

0706

ab1.

910.

068

4.00

60.

122

0.45

50.

028

0.23

0.02

65.

62lm

0427

m14

753

ab2.

155

0.04

74.

681

0.06

40.

505

0.02

20.

330.

021

2.95

lm04

37n1

4794

ab2.

282

0.04

74.

968

0.07

50.

494

0.02

10.

271

0.01

91.

81lm

0300

m23

701

ab2.

187

0.04

14.

731

0.05

70.

507

0.01

90.

318

0.01

82.

72lm

0425

m12

624

ab2.

302

0.04

24.

922

0.07

0.48

10.

018

0.26

70.

017

1.57

lm03

00m

2326

6ab

2.17

60.

075

4.96

70.

116

0.57

20.

038

0.32

70.

034

3.57

lm03

01n1

4847

ab2.

295

0.05

34.

417

0.14

50.

380.

018

0.12

80.

017

12.9

1lm

0435

m93

34ab

2.19

80.

043

4.74

10.

058

0.52

10.

020.

335

0.01

93.

34lm

0423

l117

40ab

2.68

10.

087

5.21

40.

199

0.35

50.

029

0.15

10.

026

3.04

lm02

91k1

0561

ab2.

136

0.04

14.

631

0.05

50.

461

0.01

70.

314

0.01

71.

62lm

0291

m11

933

ab2.

197

0.05

14.

512

0.11

80.

391

0.01

80.

152

0.01

821

.22

lm04

23n2

6224

ab2.

297

0.03

94.

966

0.05

80.

548

0.01

90.

332

0.01

82.

39lm

0302

k147

96ab

2.40

50.

054.

811

0.06

90.

450.

020.

290.

022.

7lm

0300

m11

839

ab2.

191

0.03

44.

777

0.04

80.

487

0.01

50.

311

0.01

41.

46lm

0303

l176

71ab

2.22

50.

032

4.80

10.

046

0.49

80.

014

0.31

70.

013

1.85

lm04

23l7

926

ab2.

224

0.03

54.

773

0.05

50.

456

0.01

40.

260.

014

1.41

lm04

27l1

8856

ab2.

259

0.04

64.

812

0.06

40.

466

0.02

0.30

30.

019

1.15

lm03

03m

1781

2ab

2.31

80.

038

4.86

80.

052

0.46

70.

016

0.30

10.

016

1.24

lm03

02n1

2351

ab2.

448

0.06

74.

655

0.12

20.

408

0.02

50.

199

0.02

43.

26lm

0300

k143

35ab

2.19

10.

044.

529

0.05

40.

363

0.01

30.

253

0.01

31.

51lm

0300

n272

86ab

2.23

80.

028

4.78

20.

039

0.50

40.

013

0.31

40.

012

2.06

lm03

02l1

2960

ab2.

313

0.06

4.80

30.

103

0.39

90.

022

0.22

20.

027.

43lm

0300

n210

91ab

2.24

40.

048

4.89

50.

069

0.57

30.

024

0.35

0.02

33.

05lm

0434

k900

8ab

2.35

0.03

84.

505

0.06

0.34

40.

012

0.19

0.01

22.

78lm

0301

l116

30ab

2.44

10.

041

5.02

30.

075

0.39

60.

015

0.2

0.01

43.

16lm

0300

k176

65ab

2.35

70.

048

5.03

70.

070.

537

0.02

30.

325

0.02

22.

69lm

0291

l107

75ab

2.49

10.

041

5.35

20.

061

0.58

20.

021

0.34

60.

021.

43lm

0300

m11

600

ab2.

140.

044

4.6

0.05

90.

462

0.01

90.

307

0.01

83.

5lm

0437

n150

49ab

2.13

70.

044

4.78

60.

065

0.48

90.

019

0.29

70.

018

2.07

119


0434

n137

04ab

2.27

70.

044

5.08

40.

064

0.54

30.

021

0.33

60.

021.

7lm

0427

l124

62ab

2.17

30.

072

4.46

20.

108

0.30

30.

020.

197

0.01

924

.7lm

0435

l524

7ab

2.33

20.

062

4.96

90.

150.

405

0.02

30.

155

0.02

13.

35lm

0434

m21

424

ab2.

526

0.09

94.

515

0.14

50.

295

0.02

80.

202

0.02

611

.26

lm04

37n8

455

ab2.

248

0.06

54.

503

0.07

30.

371

0.02

20.

309

0.02

39.

94lm

0444

l200

33ab

2.26

80.

131

4.81

80.

187

0.34

30.

041

0.24

10.

039

18.2

7lm

0293

n208

70ab

2.26

80.

039

4.81

0.04

90.

450.

016

0.33

10.

016

2.43

lm04

37m

2088

3ab

2.27

10.

039

4.89

30.

057

0.49

30.

017

0.29

70.

017

1.82

lm02

93m

1962

8ab

2.33

80.

039

5.18

20.

059

0.50

80.

018

0.29

30.

017

1.86

lm03

03n1

2799

ab2.

288

0.04

74.

902

0.07

70.

424

0.01

80.

235

0.01

70.

97lm

0434

l170

31ab

2.07

80.

051

4.72

10.

071

0.55

0.02

50.

343

0.02

53.

95lm

0293

m19

003

ab2.

328

0.04

64.

826

0.05

20.

366

0.01

50.

315

0.01

68.

53lm

0437

k153

28ab

2.28

90.

042

4.89

40.

061

0.56

20.

021

0.33

60.

023.

01lm

0291

k100

47ab

2.28

70.

046

4.97

10.

067

0.55

70.

022

0.33

30.

021

2.61

lm02

93k2

5226

ab2.

438

0.03

75.

113

0.05

30.

503

0.01

70.

310.

016

0.87

lm03

03n2

7302

ab2.

539

0.04

85.

322

0.08

0.46

80.

020.

254

0.01

91.

74lm

0435

n113

21ab

2.20

10.

057

4.74

80.

095

0.38

20.

020.

211

0.01

93.

81lm

0437

k868

1ab

2.15

80.

053

4.74

20.

092

0.40

70.

020.

215

0.01

91.

86lm

0300

l207

39ab

2.27

40.

038

5.03

0.05

60.

473

0.01

60.

281

0.01

61.

76lm

0310

l181

47ab

2.18

90.

055

4.85

0.08

0.49

40.

024

0.30

70.

024

3.06

lm03

02l2

6417

ab2.

304

0.05

34.

974

0.07

20.

548

0.02

60.

353

0.02

52.

64lm

0310

k180

10ab

2.28

60.

034

4.97

80.

050.

529

0.01

60.

311

0.01

52.

12lm

0300

k165

63ab

2.30

30.

037

5.04

10.

057

0.51

60.

017

0.29

20.

016

1.91

lm03

03m

2124

5ab

2.17

60.

044

4.84

30.

065

0.49

60.

020.

301

0.01

92.

53lm

0437

k139

06ab

2.50

80.

054

5.37

20.

090.

476

0.02

30.

264

0.02

10.

62lm

0293

m17

000

ab2.

356

0.03

95.

070.

058

0.47

80.

017

0.29

0.01

60.

86lm

0435

m70

58ab

2.16

60.

069

4.55

10.

110.

332

0.02

10.

184

0.02

27.

92lm

0425

m42

88ab

2.33

40.

061

4.95

50.

109

0.48

10.

026

0.24

50.

024

2.13

lm04

35n1

3913

ab2.

475

0.06

15.

398

0.12

80.

377

0.02

10.

171

0.01

921

.96

lm04

26m

2441

4ab

2.50

20.

071

5.44

70.

121

0.44

90.

029

0.25

10.

026

1.19

lm04

25l1

0247

ab2.

221

0.04

64.

869

0.06

90.

487

0.02

0.29

20.

019

1.63

lm03

10k1

5738

ab2.

216

0.08

14.

521

0.18

40.

270.

020.

117

0.02

17.1

3lm

0435

k123

09ab

2.29

10.

046

4.99

30.

069

0.45

90.

019

0.28

30.

019

1.05

120


0435

l985

8ab

2.25

30.

068

4.94

10.

103

0.49

60.

030.

292

0.02

92.

21lm

0434

k730

2ab

2.66

70.

055

5.65

0.08

40.

536

0.02

70.

295

0.02

60.

59lm

0293

l126

31ab

2.41

30.

044

5.22

40.

069

0.49

80.

020.

290.

019

0.84

lm04

35k1

7589

ab2.

509

0.06

15.

342

0.09

80.

480.

026

0.27

80.

024

0.76

lm02

93l5

252

ab2.

340.

047

5.21

0.07

40.

471

0.02

0.27

20.

019

1.94

lm03

12k4

503

ab2.

686

0.07

45.

942

0.14

20.

498

0.03

30.

238

0.02

99.

81lm

0436

k158

55ab

2.15

50.

074

5.56

60.

182

0.50

30.

033

0.17

90.

028

7.97

lm04

25l2

1048

ab2.

228

0.03

94.

743

0.05

40.

492

0.01

70.

316

0.01

72.

05lm

0427

m20

466

ab2.

339

0.06

45.

102

0.13

50.

452

0.02

60.

195

0.02

34.

15lm

0435

k120

02ab

2.52

10.

046

5.40

90.

066

0.54

0.02

20.

326

0.02

10.

7lm

0424

n522

7ab

2.21

10.

048

4.78

10.

067

0.55

0.02

30.

349

0.02

23.

64lm

0437

m97

13ab

2.23

40.

039

4.77

20.

058

0.49

20.

017

0.29

40.

017

2.27

lm03

03l2

6148

ab2.

467

0.05

65.

202

0.09

50.

438

0.02

20.

240.

021

1.01

lm03

02k1

3534

ab2.

424

0.05

5.17

90.

082

0.48

10.

021

0.26

60.

020.

87lm

0305

k570

4ab

2.47

80.

065

5.33

40.

112

0.44

30.

026

0.23

40.

024

0.87

lm04

37l1

5735

ab2.

287

0.06

25.

199

0.10

80.

430.

025

0.21

10.

024

2.76

lm04

34m

1964

8ab

2.47

90.

054

5.24

80.

095

0.40

80.

020.

214

0.01

90.

98lm

0300

n139

61ab

2.32

70.

029

4.92

50.

041

0.51

0.01

30.

325

0.01

31.

03lm

0303

l276

10ab

2.38

90.

061

5.24

90.

101

0.41

70.

023

0.23

40.

022

1.37

lm02

92n2

2612

ab2.

614

0.08

25.

327

0.16

50.

432

0.03

20.

204

0.02

91.

71lm

0293

n182

29ab

2.38

10.

065

5.31

0.11

60.

437

0.02

60.

222

0.02

51.

85lm

0303

n974

5ab

2.65

20.

074

5.85

20.

233

0.48

20.

032

0.13

80.

028

37.0

3lm

0435

m18

273

ab2.

603

0.07

85.

695

0.38

60.

402

0.02

90.

080.

025

12.4

3lm

0423

l211

78ab

2.19

40.

067

5.05

70.

112

0.43

50.

026

0.24

50.

024

2.9

lm03

03n1

6102

ab2.

418

0.03

25.

128

0.04

50.

516

0.01

50.

315

0.01

40.

97lm

0424

n125

43ab

2.39

0.03

55.

115

0.05

10.

503

0.01

60.

306

0.01

60.

71lm

0300

n199

27ab

2.56

50.

083

5.37

80.

149

0.40

30.

031

0.19

80.

031

1.03

lm03

00l2

5566

ab2.

454

0.06

5.31

60.

10.

399

0.02

20.

226

0.02

11.

11lm

0435

k158

16ab

2.29

70.

045

5.02

30.

067

0.47

20.

019

0.28

90.

018

1.21

lm03

00k1

1860

ab2.

484

0.05

75.

302

0.12

10.

428

0.02

20.

184

0.02

1.94

lm03

03m

1100

5ab

2.37

40.

035.

249

0.04

40.

528

0.01

40.

320.

013

2.12

lm03

01n1

4943

ab2.

391

0.09

84.

398

0.32

60.

379

0.03

40.

111

0.03

8.01

lm04

36m

1701

1ab

2.53

70.

046

5.27

80.

078

0.50

20.

021

0.27

10.

019

1.03

121


0301

l227

86ab

2.46

70.

048

5.26

60.

075

0.48

40.

021

0.27

70.

019

0.7

lm04

36n8

236

ab2.

313

0.05

74.

707

0.07

40.

458

0.02

40.

314

0.02

43.

22lm

0300

m25

109

ab2.

382

0.03

55.

290.

056

0.53

60.

017

0.29

10.

016

2.43

lm03

10l1

6334

ab2.

532

0.10

95.

045

0.65

40.

375

0.03

70.

066

0.03

119

.71

lm02

93l2

5506

ab2.

207

0.03

54.

869

0.04

90.

469

0.01

50.

30.

015

1.47

lm03

10l1

4484

ab2.

369

0.04

55.

118

0.06

30.

519

0.02

10.

321

0.02

1.76

lm03

01l2

5140

ab2.

371

0.03

45.

009

0.04

80.

552

0.01

70.

340.

016

2.65

lm02

91l2

6545

ab2.

413

0.03

35.

188

0.04

90.

545

0.01

60.

324

0.01

51.

38lm

0434

n841

3ab

2.58

0.04

85.

441

0.07

60.

521

0.02

20.

293

0.02

10.

64lm

0300

n120

88ab

2.40

50.

041

5.32

0.07

0.55

60.

020.

287

0.01

81.

74lm

0427

k174

52ab

2.31

70.

075

5.30

60.

142

0.44

40.

030.

221

0.02

74.

07lm

0300

n121

09ab

2.48

60.

043

5.29

70.

066

0.48

90.

019

0.27

50.

018

0.63

lm04

26n9

666

ab2.

435

0.19

4.89

70.

355

0.16

60.

030.

096

0.02

748

.54

lm04

34n2

2292

ab2.

656

0.08

65.

484

0.17

80.

501

0.03

90.

218

0.03

45.

84lm

0303

m56

51ab

2.59

50.

055

5.38

60.

107

0.46

70.

023

0.22

10.

022.

12lm

0301

m15

788

ab2.

339

0.08

65.

239

0.13

30.

452

0.03

50.

279

0.03

36.

1lm

0305

m38

82ab

2.54

0.05

5.33

0.07

80.

474

0.02

10.

277

0.02

0.78

lm03

05m

7850

ab2.

598

0.09

95.

338

0.19

90.

309

0.02

90.

151

0.02

616

.23

lm04

27m

6338

ab2.

543

0.05

25.

259

0.11

10.

479

0.02

30.

204

0.01

912

.2lm

0434

n173

83ab

2.40

40.

086

5.61

10.

224

0.37

30.

029

0.13

60.

026

5.61

lm03

01l1

6487

ab2.

667

0.14

96.

226

0.59

90.

322

0.04

40.

087

0.03

844

.37

lm03

00l2

3462

ab2.

440.

047

5.29

10.

073

0.49

90.

021

0.28

60.

020.

88lm

0310

l189

11ab

2.59

0.07

15.

605

0.18

80.

415

0.02

70.

145

0.02

44.

97Ta

ble

6.4:

Four

ierp

aram

eter

soft

he25

1co

nfirm

edR

RLy

rae

star

sin

tile

LMC

8_3.

122


6.4 Metallicity of the RR Lyrae stars in tile LMC 8_3

Spectroscopically determined metallicities are not available for the RR Lyrae stars in tile

LMC 8_3, so we estimated individual photometric metal abundances from the Fourier pa-

rameters of the light curves (see Subsection 1.5.1). In particular, we applied Eqs. 1.11 and

1.13 to derive the metallicity of RRab and RRc stars, respectively, and Eq. 1.12 to obtain

the φ31 Fourier parameters in the Kepler magnitudes.

Following Cacciari et al. (2005) and Kapakos et al. (2011) we only considered RRab

stars for which Dm < 5 (132 RRab stars) and RRc stars for which σ(φ31) < 0.3 (20 RRc

stars). Among the RRc stars we also discarded:

• lm0437m22126, since it has a positive value of metallicity ([Fe/H] = 0.490±0.368

dex), out of the range of typical metallicities of RR Lyrae stars in the LMC;

• lm0300l14647. This star was classified as RRc by us, and as RRd by OGLE III.

• lm0293n31080 - RRc according to our classification, but RRab according to the

OGLE III catalogue. Since the classification of this star is doubtful we discarded

this star from the following analysis. However, it should be noted that if the star were

considered as an RRab its Dm value would be larger than 5, hence, its photometric

metallicity would not be reliable.

Individual photometric metallicities for the 132 RRab stars and 17 RRc stars are pre-

sented in Tables 6.5 and 6.6, respectively. They are all on the Carretta et al. (2009) metallic-

ity scale. The weighted mean metallicity of the RRab stars in tile LMC 8_3 is: ⟨[Fe/H]C09⟩ =

(−1.58 ± 0.01) dex , σ = 0.5, average on 132 stars. The weighted mean metallicity mean

of the RRc stars is: ⟨[Fe/H]C09⟩ = (−1.82 ± 0.04) dex, σ = 0.3, average on 17 stars.

There is a systematic difference of ∼ 0.25 dex between the two mean metallicities, with the

RRab stars being more metal rich. Nemec et al. (2013) calibrated Eq. 1.11 using accurate

pulsation periods, Fourier light curve parameters and spectroscopic metal abundances of 37

field RRab stars observed by the Kepler satellite. Instead the sample of Kepler-field RRc

stars contained only four objects, so it was not possible to derive independently a relation

similar to Eq. 1.11 for the RRc stars. Nemec et al. (2013) added the four Kepler-RRc stars

to the sample of 106 RRc stars in 12 globular clusters analysed by Morgan et al. (2007),

who derived the P − φ31 − [Fe/H] relation on the range of metallicities from -2.2 to -1.0

123

6.4. METALLICITY OF THE RR LYRAE STARS IN TILE LMC 8_3

dex. Nemec et al. (2013) obtained Eq. 1.13 by recalibrating Morgan et al. (2007)’s relation.

Some systematics in the calibration of the two different relations used to estimate the metal-

licity of the RRab and RRc stars could be the cause of the systematic offset of ∼ 0.25 dex

we find between the metallicity of RRab and RRc stars in tile LMC 8_3.

124


ERO

S-2

idPe

riod

φ31(V

)φ31_k

epEr

rorφ

31_k

ep[F

e/H] C

09

Erro

r[Fe/H] C

09

Dm

(day

s)(d

ex)

dex

lm04

36n8

236

0.65

0192

4.70

74.

858

0.07

8-2

.97

0.24

93.

22lm

0434

k900

80.

5676

354.

505

4.65

60.

065

-2.7

110.

22.

78lm

0300

k143

350.

5661

574.

529

4.68

0.06

-2.6

280.

184

1.51

lm04

25k1

1500

0.54

0233

4.44

14.

592

0.09

-2.5

840.

254

3.99

lm02

93l2

5506

0.65

7982

4.86

95.

020.

055

-2.5

630.

177

1.47

lm04

25l2

1048

0.61

5813

4.74

34.

894

0.06

-2.5

370.

184

2.05

lm04

37m

9713

0.62

0011

4.77

24.

923

0.06

4-2

.496

0.19

22.

27lm

0300

m11

600

0.57

0995

4.6

4.75

10.

064

-2.4

850.

191

3.5

lm04

24n5

227

0.61

9983

4.78

14.

932

0.07

2-2

.471

0.21

13.

64lm

0300

l133

120.

5274

524.

439

4.59

0.06

2-2

.444

0.18

22.

59lm

0302

n123

510.

5661

344.

655

4.80

60.

125

-2.2

90.

323

3.26

lm04

37k8

681

0.58

9055

4.74

24.

893

0.09

6-2

.287

0.25

71.

86lm

0434

l170

310.

5829

374.

721

4.87

20.

076

-2.2

830.

213.

95lm

0291

k105

610.

5571

4.63

14.

782

0.06

1-2

.261

0.17

51.

62lm

0435

n113

210.

5871

834.

748

4.89

90.

098

-2.2

540.

262

3.81

lm03

01l2

5140

0.66

3184

5.00

95.

160.

055

-2.2

180.

167

2.65

lm04

25l1

0247

0.60

7461

4.86

95.

020.

074

-2.1

260.

202

1.63

lm03

00n1

3961

0.62

3548

4.92

55.

076

0.04

9-2

.12

0.14

91.

03lm

0426

n120

180.

5294

64.

594.

741

0.07

7-2

.08

0.20

41.

86lm

0303

m21

245

0.59

3551

4.84

34.

994

0.07

-2.0

70.

192.

53lm

0425

n232

500.

5251

914.

581

4.73

20.

079

-2.0

580.

207

2.73

lm03

10l1

8147

0.59

0217

4.85

5.00

10.

084

-2.0

240.

219

3.06

lm02

93n2

0870

0.57

819

4.81

4.96

10.

055

-2.0

150.

157

2.43

lm04

37n1

5049

0.57

1014

4.78

64.

937

0.07

-2.0

080.

187

2.07

lm04

27m

1475

30.

5440

14.

681

4.83

20.

069

-2.0

060.

184

2.95

lm03

00l2

3462

0.74

4314

5.29

15.

442

0.07

7-2

.004

0.22

80.

88lm

0435

k158

160.

6387

945.

023

5.17

40.

072

-1.9

930.

196

1.21

lm03

00n2

7286

0.56

6301

4.78

24.

933

0.04

7-1

.975

0.13

92.

06lm

0436

n206

280.

4931

074.

473

4.62

40.

061

-1.9

730.

166

4.37

lm04

35l9

858

0.60

9462

4.94

15.

092

0.10

6-1

.964

0.26

62.

21

125

6.4. METALLICITY OF THE RR LYRAE STARS IN TILE LMC 8_3lm

0423

l792

60.

5618

184.

773

4.92

40.

061

-1.9

550.

166

1.41

lm04

35m

9334

0.55

085

4.74

14.

892

0.06

4-1

.928

0.17

3.34

lm03

00m

1183

90.

5597

334.

777

4.92

80.

055

-1.9

260.

153

1.46

lm03

03n1

3977

0.49

9556

4.52

44.

675

0.04

9-1

.922

0.14

21.

53lm

0310

l144

840.

6616

525.

118

5.26

90.

068

-1.9

220.

188

1.76

lm03

00m

2370

10.

5461

024.

731

4.88

20.

063

-1.9

070.

167

2.72

lm03

03l1

7671

0.56

0588

4.80

14.

952

0.05

3-1

.877

0.14

81.

85lm

0427

l188

560.

5626

984.

812

4.96

30.

069

-1.8

710.

179

1.15

lm04

37k1

5328

0.58

4568

4.89

45.

045

0.06

6-1

.869

0.17

53.

01lm

0434

m61

390.

5403

584.

728

4.87

90.

055

-1.8

590.

152

2.26

lm04

23l2

1178

0.63

2125

5.05

75.

208

0.11

5-1

.858

0.28

22.

9lm

0291

n604

00.

5276

194.

677

4.82

80.

055

-1.8

540.

152.

65lm

0302

k147

960.

5596

354.

811

4.96

20.

074

-1.8

450.

187

2.7

lm04

35k1

2309

0.60

8992

4.99

35.

144

0.07

4-1

.835

0.19

1.05

lm04

37m

2088

30.

5802

874.

893

5.04

40.

063

-1.8

350.

166

1.82

lm04

25m

4288

0.59

7504

4.95

55.

106

0.11

2-1

.833

0.26

82.

13lm

0303

n127

990.

5818

484.

902

5.05

30.

081

-1.8

270.

203

0.97

lm02

91l2

6545

0.66

9488

5.18

85.

339

0.05

5-1

.801

0.15

91.

38lm

0435

k200

620.

5141

254.

654

4.80

50.

059

-1.7

730.

156

2.55

lm03

03m

1781

20.

5655

564.

868

5.01

90.

058

-1.7

660.

155

1.24

lm04

25l1

4852

0.53

6054

4.75

34.

904

0.05

1-1

.761

0.14

12.

29lm

0424

n125

430.

6353

165.

115

5.26

60.

057

-1.7

430.

157

0.71

lm03

01m

2278

00.

5354

594.

759

4.91

0.05

6-1

.742

0.15

1.26

lm03

02l2

6417

0.59

0296

4.97

45.

125

0.07

7-1

.731

0.19

2.64

lm03

00n2

1091

0.56

746

4.89

55.

046

0.07

4-1

.722

0.18

33.

05lm

0310

k180

100.

5902

994.

978

5.12

90.

056

-1.7

210.

151

2.12

lm03

05m

3882

0.71

0488

5.33

5.48

10.

082

-1.7

010.

219

0.78

lm03

02l2

3297

0.51

1473

4.67

64.

827

0.05

6-1

.697

0.14

93.

26lm

0291

k100

470.

5850

244.

971

5.12

20.

072

-1.6

950.

179

2.61

lm03

03n1

6102

0.63

2428

5.12

85.

279

0.05

2-1

.692

0.14

60.

97lm

0435

m17

793

0.52

4956

4.74

44.

895

0.05

5-1

.677

0.14

51.

3lm

0310

k112

530.

5371

494.

797

4.94

80.

068

-1.6

730.

169

2.19

lm02

93m

1437

50.

5079

954.

678

4.82

90.

048

-1.6

590.

133

2.55

126


0300

k121

840.

5248

134.

764.

911

0.06

2-1

.641

0.15

61.

69lm

0427

m20

466

0.61

6626

5.10

25.

253

0.13

7-1

.639

0.30

94.

15lm

0300

n121

090.

6834

595.

297

5.44

80.

071

-1.6

240.

187

0.63

lm03

00k1

6563

0.59

2704

5.04

15.

192

0.06

3-1

.599

0.15

91.

91lm

0300

l207

390.

5890

665.

035.

181

0.06

2-1

.596

0.15

71.

76lm

0435

l524

70.

5718

234.

969

5.12

0.15

2-1

.594

0.32

53.

35lm

0300

m17

178

0.51

8967

4.76

54.

916

0.05

5-1

.576

0.14

22.

19lm

0303

n153

220.

5057

334.

714.

861

0.05

1-1

.568

0.13

61.

76lm

0301

l242

550.

5105

84.

732

4.88

30.

054

-1.5

670.

142.

32lm

0427

k174

520.

6754

985.

306

5.45

70.

144

-1.5

560.

333

4.07

lm02

93m

1700

00.

5952

245.

075.

221

0.06

4-1

.555

0.15

90.

86lm

0437

k157

720.

4883

224.

654

4.80

50.

05-1

.515

0.13

41.

88lm

0300

n120

880.

6723

565.

325.

471

0.07

5-1

.505

0.18

71.

74lm

0423

n262

240.

5593

664.

966

5.11

70.

064

-1.5

0.15

52.

39lm

0302

k135

340.

6208

85.

179

5.33

0.08

6-1

.498

0.2

0.87

lm03

03m

1100

50.

6437

75.

249

5.4

0.05

1-1

.492

0.14

2.12

lm04

25m

1262

40.

5470

654.

922

5.07

30.

075

-1.4

920.

173

1.57

lm03

01l2

2786

0.64

8027

5.26

65.

417

0.07

9-1

.481

0.19

10.

7lm

0437

l157

350.

6225

535.

199

5.35

0.11

1-1

.466

0.24

62.

76lm

0303

m56

510.

6925

475.

386

5.53

70.

11-1

.465

0.26

22.

12lm

0291

n201

010.

5172

544.

814

4.96

50.

047

-1.4

570.

127

1.67

lm03

00m

2510

90.

6528

915.

295.

441

0.06

2-1

.457

0.15

82.

43lm

0303

m17

152

0.52

4201

4.84

44.

995

0.06

2-1

.457

0.15

2.93

lm03

01l1

1630

0.56

8156

5.02

35.

174

0.07

9-1

.45

0.18

13.

16lm

0436

l204

500.

5113

954.

792

4.94

30.

064

-1.4

490.

154

3.12

lm03

03l2

6148

0.62

0647

5.20

25.

353

0.09

8-1

.447

0.22

11.

01lm

0436

m17

011

0.64

5996

5.27

85.

429

0.08

2-1

.442

0.19

41.

03lm

0300

k176

650.

5689

975.

037

5.18

80.

075

-1.4

280.

172

2.69

lm04

35m

2356

30.

5250

484.

867

5.01

80.

095

-1.4

180.

203

4.13

lm03

00m

2326

60.

5488

684.

967

5.11

80.

119

-1.4

140.

246

3.57

lm03

00m

1932

40.

5253

124.

871

5.02

20.

064

-1.4

120.

151

3.92

lm02

93k2

5226

0.58

6479

5.11

35.

264

0.05

9-1

.40.

146

0.87

lm04

34k2

2095

0.53

9682

4.94

55.

096

0.05

6-1

.384

0.13

92.

1

127

6.4. METALLICITY OF THE RR LYRAE STARS IN TILE LMC 8_3lm

0293

l525

20.

6129

085.

215.

361

0.07

8-1

.379

0.18

1.94

lm04

37n1

4794

0.54

4769

4.96

85.

119

0.07

9-1

.379

0.17

61.

81lm

0300

k118

600.

6437

575.

302

5.45

30.

124

-1.3

770.

268

1.94

lm04

27n7

741

0.48

284

4.69

94.

850.

044

-1.3

690.

121

1.2

lm03

03l2

7610

0.62

3747

5.24

95.

40.

104

-1.3

670.

227

1.37

lm04

34m

1964

80.

6226

045.

248

5.39

90.

098

-1.3

620.

216

0.98

lm04

34n1

3704

0.57

1166

5.08

45.

235

0.06

9-1

.349

0.15

91.

7lm

0291

m87

100.

5117

454.

849

5.0

0.07

7-1

.338

0.17

1.8

lm02

93l1

2631

0.61

0866

5.22

45.

375

0.07

4-1

.337

0.17

0.84

lm04

37k2

2654

0.49

1312

4.76

44.

915

0.05

9-1

.32

0.14

12.

39lm

0434

l204

350.

4888

14.

754

4.90

50.

053

-1.3

170.

132

1.49

lm03

00l2

5566

0.63

8155

5.31

65.

467

0.10

3-1

.314

0.22

41.

11lm

0301

k175

540.

5355

674.

967

5.11

80.

065

-1.3

070.

151.

58lm

0312

k211

110.

4606

4.62

64.

777

0.05

-1.2

930.

128

2.16

lm02

93n1

8229

0.62

8127

5.31

5.46

10.

119

-1.2

680.

246

1.85

lm04

34n8

413

0.67

0871

5.44

15.

592

0.08

-1.2

30.

185

0.64

lm02

93m

1962

80.

5811

415.

182

5.33

30.

064

-1.2

260.

147

1.86

lm03

10l1

8911

0.74

8431

5.60

55.

756

0.19

-1.2

150.

431

4.97

lm02

92n2

2612

0.62

4068

5.32

75.

478

0.16

7-1

.21

0.32

31.

71lm

0300

n199

270.

6371

295.

378

5.52

90.

151

-1.1

820.

297

1.03

lm03

05k5

704

0.62

165.

334

5.48

50.

115

-1.1

820.

232

0.87

lm02

93n3

0795

0.47

4027

4.76

94.

920.

058

-1.1

50.

134

2.31

lm03

01m

1558

40.

5413

45.

088

5.23

90.

05-1

.124

0.12

21.

67lm

0435

k175

890.

6126

355.

342

5.49

30.

101

-1.1

150.

203

0.76

lm04

35k1

2002

0.61

8774

5.40

95.

560.

071

-1.0

240.

152

0.7

lm03

03n2

7302

0.58

6637

5.32

25.

473

0.08

4-1

.003

0.16

61.

74lm

0423

l117

400.

5543

375.

214

5.36

50.

201

-0.9

910.

325

3.04

lm03

02l1

2678

0.42

4945

4.59

64.

747

0.06

1-0

.983

0.13

52.

41lm

0437

k139

060.

5943

325.

372

5.52

30.

094

-0.9

590.

177

0.62

lm04

26m

2441

40.

6068

695.

447

5.59

80.

124

-0.8

960.

217

1.19

lm02

91l1

0775

0.57

0992

5.35

25.

503

0.06

6-0

.863

0.13

41.

43lm

0437

m20

444

0.51

1423

5.14

15.

292

0.06

3-0

.822

0.12

62.

07lm

0436

n111

720.

4317

334.

731

4.88

20.

049

-0.8

190.

115

1.93

128


0424

m22

887

0.39

8125

4.57

84.

729

0.06

4-0

.735

0.13

22.

21lm

0434

k730

20.

6101

925.

655.

801

0.08

8-0

.592

0.14

70.

59lm

0303

k252

100.

5249

185.

566

5.71

70.

077

-0.3

530.

112

0.87

Tabl

e6.

5:Ph

otom

etric

met

allic

ityof

132

RR

abst

ars

intil

eLM

C8_

3fo

rwhi

chD

m<

5(C

olum

n1:

ERO

S-2

iden

tifica

tion

ofth

est

ar;C

ol-

umn

2:Pe

riod

ofth

est

arfr

omth

eER

OS-

2ca

talo

gue;

Col

umn

3:Fo

urie

rpa

ram

eter

φ31

ofth

esi

neFo

urie

rde

com

posi

tion

oflig

htcu

rves

inth

eVJ

pass

band

;Col

umn

4:Fo

urie

rpar

amet

erφ31

ofth

esi

neFo

urie

rde-

com

posi

tion

inth

eK

eple

rmag

nitu

desd

eriv

edw

ithEq

.1.1

2;C

olum

n5:

Erro

rofφ

31

inth

eK

eple

rmag

nitu

des;

Col

umn

6:M

etal

licity

onth

eC

09m

etal

licity

scal

ede

rived

with

Eq.1

.11;

Col

umn

7:Er

roro

fm

etal

licity

onth

eC

09m

etal

licity

scal

e;C

olum

n8:

Dm

valu

e).

129

6.4. METALLICITY OF THE RR LYRAE STARS IN TILE LMC 8_3

ERO

S-2

idPe

riod

φc 31

errφ

c 31

[Fe/H] C

09

err[Fe/H] C

09

(day

s)(d

ex)

(dex

)lm

0300

l146

470.

4336

22.

517

0.24

9-2

.76

0.13

1lm

0293

n310

800.

4365

31.

189

0.17

-2.4

830.

148

lm04

34l7

912

0.45

5709

0.90

10.

264

-2.3

740.

194

lm03

03m

2298

90.

4273

244.

208

0.20

4-2

.191

0.18

4lm

0300

l889

00.

3487

012.

535

0.14

9-2

.106

0.13

5lm

0425

n137

530.

3242

851.

817

0.20

4-1

.984

0.13

1lm

0305

m62

940.

3666

833.

413

0.21

6-1

.979

0.17

1lm

0312

l151

930.

3317

82.

557

0.22

4-1

.939

0.14

7lm

0425

l648

10.

3449

973.

021

0.28

1-1

.92

0.18

lm03

01m

1584

70.

3300

772.

696

0.20

6-1

.881

0.14

9lm

0425

n186

800.

3103

661.

197

0.28

5-1

.842

0.13

3lm

0434

n143

100.

2965

731.

887

0.25

-1.7

30.

137

lm02

91n2

5551

0.30

8322

2.48

60.

249

-1.7

20.

156

lm04

35m

9109

0.29

5152

2.01

60.

291

-1.6

970.

145

lm03

02n4

858

0.29

2002

2.21

20.

27-1

.623

0.15

2lm

0303

n315

830.

3141

83.

146

0.19

8-1

.517

0.16

9lm

0291

l119

400.

3033

182.

985

0.16

7-1

.467

0.15

6lm

0300

m68

080.

3291

393.

856

0.27

4-1

.267

0.24

7lm

0424

m19

442

0.30

4605

-0.5

60.

284

-1.0

510.

232

lm04

37m

2212

60.

2806

844.

919

0.27

70.

490.

368

Tabl

e6.

6:Ph

otom

etric

met

allic

ityof

20R

Rc

star

sin

tile

LMC

8_3

(Col

-um

n1:

ERO

S-2

iden

tifica

tion

ofth

est

ar;C

olum

n2:

Perio

d;C

olum

n3:

Four

ierp

aram

eter

φc 31

ofth

eco

sine

Four

ierd

ecom

posi

tion;

Col

umn

4:Er

roro

fφc 31;C

olum

n5:

Met

allic

ityin

the

C09

met

allic

itysc

ale

deriv

edw

ithEq

.1.

13;

Col

umn

6:Er

ror

ofm

etal

licity

inth

eC

09m

etal

licity

scal

e).

130


6.5 Ks magnitude of the RR Lyrae stars in tile LMC 8_3

We built the Ks-band light curves of the 251 confirmed RR Lyrae stars in tile LMC 8_3,

using the Ks aperture photometry of the VMC data provided by the VSA internal release

of 5 August 2013. In order to derive the mean ⟨Ks⟩ magnitudes we fitted the light curves

of the RR Lyrae stars with the templates from Jones et al. (1996). This method requires a

precise knowledge of the ephemerides and amplitudes in the VJ band, for which we used

the values derived in our analysis of the EROS-2 light curves with GRATIS (see Table 6.2).

We also corrected for any phase shift between templates and data points.

To correct the mean magnitudes for reddening we adopted the mean value of the ex-

tinction in the V band for tile LMC 8_3 derived by Rubele et al. (2012) and applied the

relation AK/AV = 0.114 from Cardelli et al. (1989). The absorption the K band is then

AK = 0.038± 0.006 mag. Dereddened mean Ks magnitudes of the 251 RR Lyrae stars are

presented in Table 6.7.

131

6.5. KS MAGNITUDE OF THE RR LYRAE STARS IN TILE LMC 8_3

VM

Cid

ERO

S-2

idR

AD

ECR

Rty

pePe

riod

Ks,0

σK

s,0

(deg

)(d

eg)

(day

s)(m

ag)

(mag

)V

MC

J050

223.

44-6

5293

6.47

lm04

23l2

0069

75.5

9747

-65.

4933

9c

0.29

1086

18.4

060.

019

VM

CJ0

5001

7.74

-652

810.

85lm

0422

n169

9375

.073

83-6

5.46

963

c0.

3607

2618

.06

0.02

1V

MC

J050

123.

87-6

5300

7.76

lm04

23l1

7670

75.3

4933

-65.

5021

c0.

3375

9418

.201

0.02

3V

MC

J050

917.

20-6

5362

8.82

lm04

35m

9109

77.3

2164

-65.

6079

8c

0.29

5152

18.2

450.

023

VM

CJ0

5095

7.20

-653

705.

78lm

0435

m10

888

77.4

8819

-65.

6182

4c

0.28

9555

18.5

060.

029

VM

CJ0

5034

6.01

-653

343.

72lm

0425

m33

5575

.941

57-6

5.56

209

c0.

3588

6418

.207

0.02

3V

MC

J050

921.

39-6

5381

4.14

lm04

35m

1353

377

.339

03-6

5.63

724

c0.

3542

7418

.118

0.02

1V

MC

J051

015.

38-6

5400

0.96

lm04

35m

1828

077

.563

86-6

5.66

69c

0.34

5305

18.1

490.

021

VM

CJ0

5021

3.12

-653

430.

92lm

0425

k462

575

.554

53-6

5.57

518

c0.

3355

3718

.285

0.02

4V

MC

J050

311.

74-6

5355

0.23

lm04

25m

8144

75.7

9879

-65.

5972

5c

0.37

6376

18.1

240.

021

VM

CJ0

5013

5.53

-653

609.

22lm

0425

k820

775

.397

93-6

5.60

249

c0.

3821

1117

.834

0.01

7V

MC

J050

153.

40-6

5363

5.13

lm04

25k9

319

75.4

7239

-65.

6096

7c

0.31

9697

18.4

180.

027

VM

CJ0

5055

4.38

-654

202.

05lm

0434

m22

078

76.4

7651

-65.

7005

c0.

3721

5718

.17

0.02

1V

MC

J051

059.

57-6

5460

0.06

lm04

44l9

270

77.7

4804

-65.

7666

5c

0.37

4023

18.0

920.

02V

MC

J050

025.

52-6

5404

1.56

lm04

24m

1944

275

.106

27-6

5.67

82c

0.30

4605

18.4

140.

028

VM

CJ0

5054

5.16

-654

541.

03lm

0434

l791

276

.438

11-6

5.76

134

c0.

4557

0918

.421

0.02

7V

MC

J050

649.

59-6

5481

1.93

lm04

34n1

4310

76.7

0655

-65.

8032

7c

0.29

6573

18.4

30.

027

VM

CJ0

5011

4.82

-654

437.

48lm

0425

l648

175

.311

67-6

5.74

371

c0.

3449

9718

.149

0.02

2V

MC

J050

214.

04-6

5461

8.69

lm04

25l1

0656

75.5

5837

-65.

7718

1c

0.34

5737

18.2

510.

024

VM

CJ0

5025

7.13

-654

724.

98lm

0425

n137

5375

.738

-65.

7902

c0.

3242

8518

.365

0.02

6V

MC

J050

308.

15-6

5480

6.87

lm04

25n1

5519

75.7

8383

-65.

8018

4c

0.30

7507

18.3

190.

024

VM

CJ0

5034

2.51

-654

918.

48lm

0425

n186

8075

.927

-65.

8217

3c

0.31

0366

18.3

960.

026

VM

CJ0

5052

0.41

-655

122.

21lm

0434

l201

6876

.335

03-6

5.85

612

c0.

3534

5218

.322

0.02

5V

MC

J050

532.

60-6

5530

6.83

lm04

34l1

9810

76.3

8578

-65.

8851

9c

0.37

9506

17.5

680.

013

VM

CJ0

5020

0.28

-655

027.

73lm

0425

l205

1375

.501

09-6

5.84

096

c0.

2899

7318

.142

0.02

2V

MC

J050

456.

47-6

5524

1.83

lm04

34l2

3190

76.2

3528

-65.

8782

7c

0.32

2595

18.2

410.

024

VM

CJ0

5015

1.53

-655

203.

97lm

0425

l243

8975

.464

57-6

5.86

768

c0.

2813

8818

.327

0.02

4V

MC

J050

654.

27-6

5575

7.68

lm04

36m

8308

76.7

2609

-65.

9659

9c

0.33

1619

18.2

530.

023

VM

CJ0

5063

7.75

-655

947.

19lm

0436

m11

977

76.6

5728

-65.

9963

7c

0.38

2103

18.1

920.

022

VM

CJ0

5093

5.73

-660

411.

25lm

0437

m22

126

77.3

9874

-66.

0697

3c

0.28

0684

18.5

330.

03

132

CHAPTER 6. RR LYRAE STARS IN THE VMC TILE LMC 8_3V

MC

J050

110.

80-6

5590

4.57

lm04

27k1

0785

75.2

9491

-65.

9845

4c

0.35

837

18.0

990.

02V

MC

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139

6.6. DISTANCE TO THE TILE LMC 8_3 FROM RR LYRAE STARS

6.6 Distance to the tile LMC 8_3 from RR Lyrae stars

In Chapter 5 we derived a new PLKsZ relation based on a sample of the 71 RR Lyrae stars

in tile LMC 5_5. We can apply the new relation, as well as other PLKsZ relations in the

literature, to estimate the distance to each VMC tile, separately. This will, in turn, allow us

to study the structure of the LMC.

In this section we describe preliminary results we have obtained from the application of

the PLKsZ relations to the RR Lyrae stars in the VMC tile LMC 8_3. Once we have period

and dereddened mean Ks magnitude for each RR Lyrae star (Table 6.7), we can immediately

plot the PL relation. This is shown in Figure 6.4, where filled and open circles are RRab

and RRc stars, respectively. We computed a weighted PLKs relation through the data by

progressively discarding objects which deviate more than 3σ from the linear regression:

Ks,0 = (−2.40 ± 0.13)logP + (17.38 ± 0.03) (6.1)

Figure 6.4 shows only objects that are located within 3σ from the best fit line. The slope

of Eq. 6.1 differs from the slope in logP derived for the 71 RR Lyrae stars in tile LMC 5_5

(Eq. 5.3), but is still consistent with it within the errors. The zero-points of Eqs. 6.1 and 5.3

are consistent within the errors, even if Eq. 6.1 does not take into account the metallicity.

A number of different PLKsZ relations exist in the literature (see Section 1.5.2): Bono

et al. (2003) (see Eq. 6.4), Dall’Ora et al. (2004) (see Eq. 6.5), Sollima et al. (2006) (see

Eq. 6.3), Sollima et al. (2008) (see Eq. 6.2), Del Principe et al. (2006) (see Eq. 6.6),

Borissova et al. (2009) (see Eq. 6.7). Benedict et al. (2011) have estimated zero-points for

all these PLKsZ relations, based on their HST trigonometric parallaxes for five Galactic

field RR Lyrae stars:

MK = (−2.38 ± 0.04)(logP + 0.28) + (0.08 ± 0.11)([Fe/H] + 1.58) + a1, (6.2)

MK = (−2.38 ± 0.04)(logP + 0.28) + a2, (6.3)

MK = −2.101(logP + 0.28) + (0.231 ± 0.012)([Fe/H] + 1.58) + a3, (6.4)

MK = (−2.16 ± 0.09)(logP + 0.28) + a4, (6.5)

MK = (−2.71 ± 0.12)(logP + 0.28) + (0.12 ± 0.04)([Fe/H] + 1.58) + a5 (6.6)

MK = (−2.11 ± 0.17)(logP + 0.28) + (0.05 ± 0.07)([Fe/H] + 1.58) + a6 (6.7)

140


where the a1 - a6 values are: −0.56 ± 0.02, −0.57 ± 0.03, −0.58 ± 0.04, −0.56 ± 0.02,

−0.57 ± 0.02, and −0.56 ± 0.03, respectively. They were derived by fitting the Lutz-

Kelker-Hanson-corrected absolute magnitudes to the equations (Benedict et al., 2011). The

different PLKsZ relations are based on a number of different metallicity scales. In particu-

lar, Bono et al. (2003) and Del Principe et al. (2006) use the Zinn & West metallicity scale.

Sollima et al. (2008) use the Carretta & Gratton (1997) metallicity scale. The relations

from Dall’Ora et al. (2004) and Sollima et al. (2006) do not have metallicity terms. Finally,

Borissova et al. (2009) use the same metallicity scale adopted by Gratton et al. (2004).

We add to the above literature relations (Eqs. 6.2-6.7) our own PLKsZ relation derived

using the dereddened mean Ks magnitudes of the 71 RR Lyrae stars in tile LMC 5_5, spec-

troscopically determined metallicities from Gratton et al. (2004) and accurately estimated

periods from the OGLE III catalogue (see Chapter 5):

MK = (−2.70 ± 0.22)logP + (0.03 ± 0.06)[Fe/H] + (−1.27 ± 0.08) (6.8)

The zero-point of our relation is also calibrated on the Benedict et al. (2011)’s HST

trigonometric parallaxes for RR Lyrae stars and the metallicity is on Gratton et al. (2004)

scale, hence, on average, 0.06 dex higher than Zinn & West’s. To derive the distance to

tile LMC 8_3 we entered the above relations using: periods for the RR Lyrae stars taken

from the EROS-2 catalogue, mean ⟨Ks⟩ dereddened magnitudes estimated as described in

Section 6.5, and metallicities obtained by the Fourier analysis of the V band light curves

(see Section 6.4).

In order to take into account the systematic difference of ∼ 0.25 dex between the mean

metallicities of RRab and RRc stars, we used three different approaches:

• We used the mean metallicity derived by averaging the photometric metallicities of

both RRab and RRc stars. We associated to the mean value obtained in this way

an error corresponding to the standard deviation of the distribution ⟨[Fe/H]C09⟩ =

−1.61; σ[Fe/H]C09= 0.4. Then we used the whole sample of 241 RRab and RRc stars

in tile LMC 8_3 to estimate the distance.

• We used the mean metallicities determined by averaging the photometric metallicities

obtained only for RRab stars. We associate to this mean value an error corresponding

to the standard deviation of the average: ⟨[Fe/H]C09ab⟩ = −1.58; σ[Fe/H]C09ab= 0.5,

141


and inferred distance moduli from the above PLKsZ relations for each of the 167

ab-type RR Lyrae stars.

• We used the mean metallicity derived by averaging the photometric metallicities ob-

tained only from the RRc stars. We associated to this mean value an error correspond-

ing to the standard deviation of the average: ⟨[Fe/H]C09c⟩ = −1.82; σ[Fe/H]C09c=

0.3, and inferred distance moduli from the above PLKsZ relations for each of the 74

c-type RR Lyrae stars.

The derived mean metallicities are on the Carretta et al. (2009) metallicity scale. To

transform them to the Zinn & West metallicity scale, used in the majority of the PLKsZ

relations listed above we applied the transformation equation provided by Carretta et al.

(2009):

[Fe/H]C09 = (1.105 ± 0.061)[Fe/H]ZW + 0.160 (6.9)

To transform the mean metallicities on the Zinn & West scale to the metallicity scale of

Eq. 6.8, we simply added 0.06 dex (Gratton et al., 2004). In order to determine the mean

metallicities on the Carretta & Gratton (1997) metallicity scale we applied the relation from

Carretta et al. (2009):

[Fe/H]C09 = (1.137 ± 0.060)[Fe/H]GC97 − 0.003 (6.10)

Each of the above PLKsZ relations (Eqs. 6.2-6.8) was used to infer the MK absolute

magnitude for each RR Lyrae star in tile LMC 8_3. The MK values were combined with

the dereddened apparent K magnitude providing a distance modulus estimate µ0 for each

individual star. Average µ0 values and related standard errors inferred from the different

PLKsZ relations are summarized in Table 6.8.

In Chapter 5 we applied our PLKsZ relation with zero-point based on the HST paral-

laxes for RR Lyrae stars by Benedict et al. (2011) to 71 RR Lyrae stars in tile LMC 5_5

and determined the mean distance µ0 = 18.71 ± 0.01 mag, which can now be compared

with the average distance to tile LMC 8_3 : µ0 = 18.615± 0.006 mag. Taken at face value

these results indicate that the external tile LMC 8_3 is located 0.1 mag closer to us than the

central tile LMC 5_5. These results are preliminary and need to be further confirmed, still

they are promising. Combining them with results obtained from the RR Lyrae stars in other

142


PLK -relation µ0(< ab >) µ0(< c >) µ0(< ab+ c >)mag mag mag

Bono et al 2003 18.623 ± 0.164 18.696 ± 0.192 18.636 ± 0.173Dall’Ora et al. 2004 18.596 ± 0170 18.610 ± 0.193 18.600 ± 0.176Sollima et al. 2008 18.596 ± 0.165 18.596 ± 0.200 18.594 ± 0.174Sollima et al. 2006 18.622 ± 0.164 18.612 ± 0.197 18.619 ± 0.174Del Principe et al. 2006 18.632 ± 0.165 18.618 ± 0.195 18.624 ± 0.174Borissova et al. 2009 18.600 ± 0.165 18.632 ± 0.186 18.607 ± 0.171Relation from this study 18.634 ± 0.159 18.605 ± 0.195 18.625 ± 0.170average 18.615 ± 0.006 18.625 ± 0.013 18.615 ± 0.006

Table 6.8 Distance moduli of tile LMC 8_3 obtained applying different PLKsZ relations tothe RR Lyrae stars in this tile (Column 1: References for the PLKsZ relations; Column 2:Distance modulus obtained using only RRab stars; Column 3: Distance modulus obtainedusing only RRc stars; Column 4: Distance modulus obtained using all the ab and c-type RRLyrae stars in tile LMC 8_3. See text for details).

VMC tiles we will be able to map the internal structure of the LMC as traced by the old

population stars.

143


Figure 6.4 Dereddened mean Ks magnitudes versus LogP for RR Lyrae stars in tile LMC

8_3. Empty and filled circles represent RRc and RRab stars, respectively. The periods of

RRc stars were fundamentalized by adding 0.127 to the LogP.

144

Conclusions

The main goal of this thesis was to study the geometric structure and the distance to the

Large Magellanic Cloud (LMC). To this purpose we have analysed three different types

of distance indicators: Classical Cepheids (CCs), “hot” eclipsing binaries (HEBs) and RR

Lyrae stars, which trace different sub-structures of the LMC.

Main results which we derived for the CCs are:

• We analysed 201 candidate CCs observed by the EROS-2 survey in the VMC tile

LMC 8_3. We classified the candidate CCs trough visual inspection of the light

curves. The sample was found to contain 124 bona-fide CCs, 2 candidate Anomalous

Cepheids, 58 eclipsing binaries, 13 small amplitude variables and 4 long period vari-

ables. Furthermore, in the sample of bona-fide CCs we found two double-mode CCs

and derived second periods for both of them.

• We determined main parameters (mean magnitudes, amplitudes and epochs of max-

imum light in the BEROS and REROS passbands) for all the 201 objects, checked

the periods provided by the EROS-2 survey and derived new periods for 16 of them.

The main parameters of the bona-fide CCs will be used in the future along with near-

infrared data from the VMC survey to measure the distance to the genuine CCs in this

tile.

• We developed a strategy for extracting bona-fide CCs from the EROS-2 sample of

candidate CCs which is based on the combination of colour-cuts in the CMD and

analysis of the scatter in the PL relations. This approach allowed us to extract a

sample of bona-fide CCs more than 97 % clean from contaminating sources. This

strategy will be applied in the analysis of all the external tiles of the LMC, for which

only the EROS-2 data are available.

The main results for HEBs are:

145

CONCLUSIONS

• We identified in the whole sample of the EROS-2 candidate CCs, 1768 EBs by com-

bining the colour-cut criterion and the visual inspection of the light curves. They are

composed by hot main sequence stars or blue giants, hence we classed them HEBs.

• We analysed the light curves of the 1768 HEBs and re-determined the previously

defined periods for 225 of them.

• We divided the sample of 1768 HEBs into contact-like (324) and non-contact (1444)

systems by visual inspection of their light curves and by analysis of the Fourier de-

composition parameters.

• We analysed the PL relation in the optical (REROS and I) and Ks passbands of the

contact-like HEBs in the EROS-2 sample. We did not confirm the existence of a PL

relation for contact-like HEBs.

• We found that contact EBs containing a red giant component from the OGLE III

catalogue do follow PL sequences in the I and Ks passbands. We computed the

weighted linear regression of the PL relation in the Ks passband:

Ks,0 = (−2.888 ± 0.096)log(P ) + (20.139 ± 0.171) (6.11)

with rms=0.406 mag.

There is a possible additional PL sequence located ∼ 1 mag fainter, but the number

of objects following it, is too small to allow a reliable fit.

Main results for the RR Lyrae stars in tile LMC 5_5 are:

• We analysed a sample of 71 RR Lyrae stars in this tile close to the bar of the LMC,

for which multi-epoch Ks photometry from the VMC survey, precise periods from

the OGLE III catalogue and spectroscopically determined metallicity are available.

We derived the mean Ks magnitudes of these stars by fitting templates from Jones et

al. (1996) to the VMC data.

• We derived a new PLKsZ relation for RR Lyrae stars by using a Bayesian fitting ap-

proach. The new PLKsZ relation has a number of advantages: (i) it uses multi-epoch

Ks photometry from the VMC survey to derive light curves and estimate mean Ks

magnitudes of the RR Lyrae stars, while in most studies single-epoch photometry is

146

CONCLUSIONS

used; (ii) it uses precisely determined periods from the OGLE III survey; (iii) the rela-

tion is based on a relatively large sample of the RR Lyrae stars with spectroscopically

determined metallicities in the range −2.06 < [Fe/H] < −0.63 dex (Gratton et al.,

2004); (iv) it is derived based on a Bayesian fitting approach developed specifically

for this study. This method takes into account: 1) the potentially significant intrinsic

dispersion of the data; 2) non-negligible errors in two dimensions; 3) the possibility

of inaccuracy in the formal error estimates.

• We calibrated the zero-point of our new PLKsZ relation by applying two different

techniques: (i) by using the distance to the LMC determined by Pietrzynski et al.

(2013); (ii) by applying the HST parallaxes of five MW RR Lyrae stars from Benedict

et al. (2011).

• We applied our PLKsZ relation with the zero-point calibrated from the HST paral-

laxes and derived the distance to tile LMC 5_5: (m − M)0 = 18.71 ± 0.09 mag.

This distance modulus is about 0.2 mag longer than the widely adopted value of

(m − M)0 = 18.5 mag. In future studies we suggest to use the relation with the

zero-point based on the precise distance to the LMC:

MK = (−2.70 ± 0.22)logP + (0.03 ± 0.06)[Fe/H]Har + (−1.05 ± 0.05) (6.12)

• We estimated the impact of Gaia on definition of the zero-point of the RR Lyrae

PLKsZ and MV − [Fe/H] relations. We selected 25 bright MW RR Lyrae stars and

simulated their Gaia parallaxes with observational errors. We applied a Bayesian fit-

ting approach specifically developed for this study to derive PLKsZ and MV −[Fe/H]

relations based on the simulated parallaxes. The final relations are very close to those

which were considered as "true" in the input and their zero-points have respectively

precisions of 0.03 mag and 0.005 mag.

Main results for the RR Lyrae stars in tile LMC 8_3 are:

• We analysed the sample of EROS-2 candidate RR Lyrae stars in tile LMC 8_3 and

extracted 251 bona-fide RR Lyrae variables that have a counterpart in the VMC cata-

logue.

• We classified the 251 bona-fide RR Lyrae stars based on both, the visual inspection

of the light curves and the analysis of the period-amplitude diagram. The sample

147

CONCLUSIONS

contains 167 RRab, 74 RRc and 10 RRd stars. For each star we derived mean magni-

tudes, amplitudes, epochs of maximum light in the BEROS and V passbands.

• We checked the periods provided by the EROS-survey and corrected them for four

objects. We determined the second periods for the 10 RRd stars.

• We performed the Fourier decomposition of the light curves of the 241 bona-fide

RRab and RRc variables and determined photometric metallicities from the Fourier

parameters of the light curves for 132 RRab stars and 17 RRc stars. The mean metal-

licity on the Carretta et al. (2009) metallicity scale, of the RRab stars in tile LMC

8_3 is ⟨[Fe/H]C09ab⟩ = −1.58; σ[Fe/H]C09ab= 0.5, whereas the mean metallicity

of the RRc stars is ⟨[Fe/H]C09c⟩ = −1.82; σ[Fe/H]C09c= 0.3. The mean metallic-

ity derived by averaging the photometric metallicities of both RRab and RRc stars is

⟨[Fe/H]C09⟩ = −1.61; σ[Fe/H]C09= 0.4. There is a shift of about 0.25 dex between

mean metallicities of RRab and RRc stars, the reason of which could be some sys-

tematics in the calibration of the relations used to derive the photometric metallicities.

• We fitted the Ks band light curves obtained by the VMC survey with templates from

Jones et al. (1996) and derived mean Ks magnitudes for 241 RR Lyrae stars. We

computed a weighted PLKs relation through the data:

Ks,0 = (−2.40± 0.13)logP + (17.38 ± 0.03) (6.13)

• We used the PLKsZ relations in the literature and our new PLKsZ relation computed

from 71 RR Lyrae stars in tile LMC 5_5 to determine individual distances to the 251

RR Lyrae stars in tile LMC 8_3 and derived the mean distance modulus: (m−M)0 =

18.615 ± 0.006 mag. These results show that the external tile LMC 8_3 seems to be

located 0.1 mag closer to us than the central tile LMC 5_5.

The comparison of the spatial distribution of the three different distance indicators re-

vealed the internal structure of the LMC. The RR Lyrae stars have a larger density in the

central region of the LMC, but in general they are distributed smoothly and likely trace

the halo of the galaxy. On the contrary, CCs and HEBs are strongly concentrated towards

the LMC bar and spiral arm, and almost disappear in the peripheral areas. HEBs are more

sharply concentrated toward regions of recent star formation such as 30 Doradus and Con-

stellation III, while CCs mostly follow the bar and spiral arm of the LMC.

148

CONCLUSIONS

From the analysis of the EBs we confirmed the existence of PL relations only for con-

tact EBs that contain a red giant component, while did not confirm the existence of a PL

relation for contact HEBs. The luminosity ratio of the components of the HEBs (main se-

quence stars and blue giants) can vary significantly. In contrast, in contact systems with a

red giant component, the giant dominates the luminosity while the contribution from the

secondary is usually negligible. As a consequence the PL relation of contact HEBs can be

much more scattered than the PL of contact EBs with a red giant component. In any case,

the scatter of the PL relation for EBs with a red giant component is too large to be used for

the determination of the distance.

The results from the RR Lyrae stars in tiles LMC 8_3 and 5_5 are puzzling and need

further investigation. The zero-point of the PLKsZ relation of RR Lyrae stars still remains

a controversial issue that cannot be solved with the present data. While this is not going to

affect our study of the structure of the LMC through the VMC data, for which we will use

differential distances, the absolute distance to the LMC from RR Lyrae stars can be derived

only when the RR Lyrae zero-point issue will be settled. A huge improvement in this topic is

expected with the astrometric mission Gaia which will measure the parallaxes of thousands

MW RR Lyrae stars. In this thesis we simulated Gaia parallaxes of only 25 bright Galactic

RR Lyrae stars and showed that using even a small sample of RR Lyrae stars with precisely

determined parallaxes we will be able to estimate the PLKsZ and MV − [Fe/H] relations

with a great precision, when combined with metallicity and photometry from other sources.

The zero-points of the CCs and EBs will also be recalibrated with Gaia, thus allowing a

direct and robust comparison of the the distance to the LMC as derived from independent

distance indicators.

149

Appendix A

Properties of the “hot” eclipsingbinaries in the LMC

Main properties and Fourier parameters of the light curves of 1768 HEBs in our sample are

presented in Table A.1. The table provides the EROS-2 identification numbers (column 1)

and coordinates (RA and DEC at J2000; columns 2 and 3) of the HEBs. Periods (column 4)

for the majority of stars are from the EROS-2 catalogue, while for 225 sources marked by an

asterisk, periods were recalculated in this study. Number of digits in the periods are the same

as originally listed in the EROS-2 catalogue. Mean ⟨BEROS⟩ and ⟨REROS⟩ magnitudes

are listed in columns 5 and 6, respectively. The EROS-2 team provided us values with three

digits as computed using all observations involved in the period determination (e.g. after

excluding outliers), however we rounded them to two digits to account for the typical errors

of the individual data-points which vary from 0.02 to 0.08 mag depending on magnitude.

Column 7 lists the epochs of minimum light in the REROS passband we calculated in this

study, they are listed with four digits, in agreement with the actual precision of EROS-2

HJDs (see below). Columns from 8 to 13 of Table A.1 present the parameters of the Fourier

decomposition in the REROS passband calculated in this study. HJDs provided by the

EROS-2 catalogue are accurate to within 10 s, hence, epochs of minimum light have four

digit accuracy.

Finally, Table A.2 provides information about the cross-identifications (EROS-2 and

VMC IDs) for 999 HEBs in common between the two catalogues, their periods and the Ks

and REROS magnitudes at maximum light.

151

ERO

S-2

idR

AD

ECPe

riod

⟨REROS⟩

⟨BEROS⟩

Epoc

h(m

in)

a0

a1

a2

a3

a4

a5

(J20

00)

(J20

00)

(HJD

−2,

450,

000)

(deg

)(d

eg)

(day

)(m

ag)

(mag

)lm

0555

k127

21*

76.2

287

-71.

2391

90.

8010

095

17.2

617

.08

2184

.700

90.

957

-0.0

37-0

.055

-0.0

070

-0.0

160.

0030

lm03

23n2

0546

80.4

206

-66.

8744

0.90

0708

17.2

417

.06

1851

.626

30.

879

-0.0

28-0

.167

-0.0

14-0

.062

-0.0

030

lm03

54n8

770

85.1

1371

-67.

1645

40.

9040

0317

.64

17.4

011

85.7

298

0.91

3-0

.03

-0.1

27-0

.008

0-0

.041

0.00

20lm

0193

k191

8279

.737

58-6

8.10

716

0.90

5358

17.0

516

.99

2213

.782

10.

958

-0.0

1-0

.047

-0.0

060

-0.0

240.

0060

lm03

41k8

979

83.6

6655

-66.

3030

70.

9117

2117

.00

16.7

511

73.7

244

0.88

2-0

.032

-0.1

73-0

.011

-0.0

740.

0lm

0285

n102

2973

.417

11-6

7.17

722

0.91

1792

17.0

716

.85

1532

.577

30.

973

-0.0

15-0

.02

-0.0

010

0.00

10-0

.002

0lm

0344

m26

510

83.0

365

-67.

1281

80.

9124

4517

.32

17.1

817

51.8

628

0.91

7-0

.01

-0.1

170.

0020

-0.0

520.

0060

lm00

23n1

1843

83.3

321

-69.

6220

90.

9125

6817

.46

17.3

917

01.4

807

0.85

4-0

.033

-0.1

41-0

.01

-0.0

320.

017

lm01

23m

1183

673

.493

11-6

9.46

511

0.91

9332

17.1

817

.29

2519

.731

90.

97-0

.014

-0.0

37-0

.005

0-0

.013

-0.0

010

lm01

22n1

3303

72.4

6236

-69.

6452

20.

9226

0417

.17

16.9

443

8.82

730.

947

-0.0

23-0

.08

-0.0

1-0

.018

0.00

40lm

0030

n213

9184

.323

19-6

9.38

179

0.92

2672

16.8

816

.77

2304

.768

60.

883

-0.0

43-0

.153

-0.0

18-0

.046

-0.0

010

lm02

26n2

0767

84.6

0396

-69.

0012

50.

9239

4117

.65

17.4

519

75.6

799

0.91

3-0

.013

-0.1

2-0

.005

0-0

.056

-0.0

lm01

06n1

3876

76.5

4384

-70.

3435

30.

9253

4417

.51

17.3

649

8.60

620.

892

-0.0

33-0

.133

-0.0

21-0

.043

-0.0

010

lm02

31k9

063

87.1

2851

-67.

7065

30.

9279

9917

.07

16.8

410

72.8

079

0.88

-0.0

2-0

.141

-0.0

050

-0.0

310.

0020

lm01

14k6

489

74.0

4547

-69.

7893

20.

9320

9717

.54

17.4

395

2.46

630.

982

-0.0

28-0

.025

0.0

-0.0

110.

0040

lm02

83n8

062

73.6

8666

-66.

7968

40.

9389

2317

.10

16.8

122

55.5

680

0.85

5-0

.034

-0.1

98-0

.014

-0.0

71-0

.005

0lm

0214

n104

5982

.863

71-6

8.57

040.

9389

7117

.76

17.7

216

59.5

486

0.95

-0.0

13-0

.084

-0.0

020

-0.0

50.

0050

lm01

71m

1673

3*76

.183

53-6

7.74

663

0.93

9001

15.9

115

.61

1915

.751

60.

948

-0.0

010

-0.0

71-0

.002

0-0

.028

-0.0

010

lm01

27k1

2134

73.2

6783

-70.

1808

40.

9394

5417

.47

17.5

122

25.5

710

0.98

1-0

.003

0-0

.046

-0.0

-0.0

29-0

.0lm

0215

l150

0483

.632

46-6

8.59

249

0.94

0678

17.2

417

.06

2200

.784

90.

912

-0.0

050

-0.1

41-0

.003

0-0

.08

-0.0

010

lm00

43k2

3371

86.9

9351

-69.

5312

0.94

1374

17.4

517

.43

1478

.771

70.

902

-0.0

31-0

.114

-0.0

11-0

.043

-0.0

010

lm03

42k1

8196

82.8

9531

-66.

7500

20.

9414

4717

.03

16.8

243

4.80

950.

911

-0.0

060

-0.1

11-0

.001

0-0

.045

-0.0

050

lm03

46l1

4981

82.7

9685

-67.

5609

0.94

1548

17.0

417

.07

1657

.518

40.

985

-0.0

25-0

.035

-0.0

11-0

.017

-0.0

lm04

66k2

3468

81.4

0389

-66.

0712

60.

9430

3217

.24

17.0

411

40.6

191

0.86

7-0

.04

-0.1

86-0

.018

-0.0

55-0

.007

0lm

0167

m21

114

74.7

5322

-68.

8346

70.

9431

8917

.76

17.5

933

6.87

080.

956

-0.0

2-0

.055

-0.0

060

-0.0

32-0

.002

0lm

0436

n210

3676

.816

2-6

6.20

443

0.94

4593

17.1

916

.93

1866

.612

50.

874

-0.0

31-0

.156

-0.0

12-0

.042

-0.0

040

lm03

41k1

8581

83.7

3331

-66.

3684

0.94

7627

17.3

717

.22

1981

.624

20.

985

-0.0

33-0

.006

0-0

.005

0-0

.005

00.

0030

lm03

41k4

660

83.6

1982

-66.

2723

10.

9533

7417

.34

17.0

918

69.6

179

0.93

2-0

.007

0-0

.107

-0.0

11-0

.069

-0.0

050

lm02

17m

1920

884

.090

04-6

8.82

472

0.95

4486

16.9

817

.01

2338

.661

70.

976

-0.0

24-0

.031

-0.0

040

-0.0

030

0.0

lm00

30n1

9548

84.4

7044

-69.

3371

10.

9552

6117

.09

16.9

321

67.8

026

0.94

2-0

.005

0-0

.077

-0.0

010

-0.0

31-0

.001

0lm

0090

n162

4378

.417

69-6

9.30

601

0.95

6439

16.9

216

.90

2198

.668

90.

953

-0.0

080

-0.0

7-0

.005

0-0

.04

-0.0

020

lm03

40m

1585

283

.069

71-6

6.35

575

0.95

8465

17.4

617

.28

2310

.712

70.

979

-0.0

62-0

.019

-0.0

17-0

.006

00.

0070

lm00

72n1

2336

92.5

0478

-69.

6507

50.

9593

17.6

117

.47

1784

.868

20.

91-0

.042

-0.1

28-0

.019

-0.0

580.

0010

lm01

02m

1044

176

.453

63-6

9.46

743

0.96

0451

17.2

216

.96

2496

.822

20.

859

-0.0

1-0

.226

0.00

50-0

.089

0.00

40lm

0015

k638

380

.934

04-6

9.79

310.

9641

5917

.16

16.9

777

2.83

830.

879

-0.0

090

-0.1

66-0

.007

0-0

.073

-0.0

010

lm05

42k2

0454

72.9

0434

-70.

9645

80.

9658

3817

.37

17.3

216

59.4

784

0.97

5-0

.048

-0.0

39-0

.032

-0.0

2-0

.004

0lm

0034

k102

3883

.799

16-6

9.82

040.

9689

8817

.19

17.2

821

60.7

476

0.92

-0.0

3-0

.122

-0.0

1-0

.056

0.00

10lm

0160

m26

440

73.5

2748

-67.

8170

20.

9691

5817

.74

17.7

314

93.6

251

0.96

1-0

.014

-0.0

360.

0020

-0.0

030

0.0

152

APPENDIX A. PROPERTIES OF THE “HOT” ECLIPSING BINARIES IN THE LMClm

0355

n118

6686

.035

32-6

7.17

845

0.96

9348

17.2

217

.08

1774

.920

30.

98-0

.056

-0.0

3-0

.02

-0.0

1-0

.008

0lm

0604

l157

3385

.467

77-7

1.41

346

0.97

6899

17.8

217

.67

1179

.844

70.

957

-0.0

26-0

.065

-0.0

17-0

.027

-0.0

090

lm00

93k1

6356

79.0

9752

-69.

4890

80.

9771

8617

.00

16.9

555

4.53

240.

926

-0.0

17-0

.105

-0.0

060

-0.0

32-0

.001

0lm

0321

l271

5880

.227

24-6

6.57

613

0.97

7509

17.2

817

.14

1236

.602

50.

937

-0.1

25-0

.086

-0.0

54-0

.025

0.00

10lm

0352

m18

009

85.0

8721

-66.

7491

90.

9789

6317

.81

17.6

111

42.7

253

0.96

6-0

.001

0-0

.05

-0.0

040

-0.0

320.

0020

lm02

23n2

6953

85.6

8687

-68.

3124

20.

9790

3417

.68

17.5

616

36.5

279

0.98

2-0

.017

-0.0

25-0

.001

0-0

.002

0-0

.0lm

0023

k200

2183

.115

16-6

9.51

038

1.01

1662

16.9

016

.89

1482

.731

10.

942

-0.0

12-0

.083

-0.0

050

-0.0

39-0

.002

0lm

0594

k127

0083

.460

81-7

1.23

035

1.01

9228

17.5

217

.56

2201

.644

30.

973

-0.0

12-0

.027

0.0

-0.0

040

0.00

20lm

0033

m10

429

85.3

568

-69.

4624

91.

0192

3217

.86

17.7

821

69.8

024

0.96

2-0

.02

-0.0

47-0

.003

0-0

.007

00.

0030

lm01

17l9

906

75.0

4975

-70.

3230

11.

0200

3417

.26

17.1

013

88.8

013

0.93

2-0

.019

-0.0

84-0

.009

0-0

.031

-0.0

060

lm00

30n2

2649

84.3

3989

-69.

3578

91.

0265

2816

.76

16.6

412

55.6

286

0.95

1-0

.007

0-0

.076

-0.0

020

-0.0

350.

0020

lm03

23l2

7434

79.9

3833

-66.

9190

21.

0272

0617

.34

17.2

217

76.8

380

0.90

9-0

.016

-0.1

21-0

.008

0-0

.055

0.00

20lm

0025

n170

9183

.559

48-6

9.99

927

1.02

8086

17.5

717

.71

1763

.812

10.

968

-0.0

15-0

.048

-0.0

11-0

.015

-0.0

010

lm01

66n2

4423

73.6

9688

-69.

0193

41.

0332

8517

.41

17.0

986

4.69

760.

952

-0.0

22-0

.038

-0.0

010

-0.0

0.0

lm04

15m

2190

274

.362

23-6

5.69

419

1.03

3457

17.6

217

.35

2241

.606

90.

957

-0.0

010

-0.0

73-0

.001

0-0

.048

-0.0

030

lm01

65n1

4065

74.7

7506

-68.

5824

31.

0380

7217

.52

17.3

448

0.76

380.

974

-0.0

23-0

.028

-0.0

010

-0.0

040

0.00

10lm

0157

l178

2172

.473

1-6

8.98

049

1.04

055

17.6

317

.47

2229

.566

00.

889

-0.0

46-0

.144

-0.0

23-0

.028

-0.0

010

lm00

91m

2706

479

.325

71-6

9.20

378

1.04

1214

17.3

216

.97

333.

8872

0.82

6-0

.048

-0.1

83-0

.013

-0.0

760.

0060

lm00

93n5

032

79.5

86-6

9.58

177

1.04

2603

16.8

416

.65

1549

.649

80.

918

-0.0

23-0

.09

-0.0

040

-0.0

22-0

.001

0lm

0405

n237

8694

.582

84-6

7.26

861

1.04

6324

16.3

916

.48

865.

7215

0.99

5-0

.02

-0.0

040

-0.0

040

-0.0

040

-0.0

020

lm01

73m

9757

76.2

3218

-68.

0513

91.

0468

816

.83

16.7

874

8.79

530.

94-0

.013

-0.0

83-0

.006

0-0

.037

-0.0

020

lm04

24n1

4561

74.9

1334

-65.

8054

51.

0472

3516

.78

16.5

320

57.4

711

0.93

3-0

.003

0-0

.093

-0.0

060

-0.0

510.

0010

lm03

17m

2435

178

.603

69-6

7.46

527

1.04

9265

17.2

417

.12

2185

.658

10.

987

-0.0

42-0

.03

-0.0

25-0

.018

-0.0

050

lm01

12n5

096

74.4

563

-69.

5837

11.

0502

2317

.77

17.6

523

27.5

878

0.87

8-0

.005

0-0

.195

0.00

40-0

.089

0.00

10lm

0493

n186

9287

.281

21-6

5.47

855

1.05

0931

17.6

317

.74

830.

8104

0.91

4-0

.041

-0.1

15-0

.018

-0.0

39-0

.003

0lm

0031

m96

5185

.603

44-6

9.10

275

1.05

1009

17.0

617

.15

2174

.803

10.

938

-0.0

060

-0.0

95-0

.001

0-0

.056

-0.0

020

lm00

11l5

712

80.9

5532

-69.

2395

11.

0512

3817

.18

16.8

922

14.6

057

0.84

5-0

.028

-0.1

86-0

.017

-0.0

57-0

.002

0lm

0244

k107

4887

.995

23-6

8.42

181.

0516

0817

.82

17.8

015

76.7

872

0.87

1-0

.039

-0.1

49-0

.018

-0.0

480.

0070

lm03

56m

2406

984

.996

3-6

7.46

769

1.05

1643

17.2

617

.11

1263

.623

40.

977

-0.0

83-0

.035

-0.0

23-0

.008

0-0

.012

lm05

40l1

5552

72.9

1439

-70.

7063

61.

0521

6517

.83

17.6

422

96.6

801

0.80

6-0

.046

-0.2

22-0

.022

-0.0

65-0

.007

0lm

0020

l855

381

.839

68-6

9.26

417

1.05

4358

17.1

516

.92

1835

.799

80.

893

-0.0

010

-0.1

61-0

.004

0-0

.087

0.00

10lm

0367

n188

0587

.432

52-6

7.60

061

1.05

5955

17.6

617

.47

2353

.670

90.

962

-0.0

35-0

.07

-0.0

18-0

.039

0.00

50lm

0311

l960

678

.420

94-6

6.46

266

1.05

9117

16.5

316

.32

1858

.840

90.

93-0

.021

-0.0

98-0

.008

0-0

.027

-0.0

lm03

56m

1026

484

.894

58-6

7.37

154

1.05

9355

17.1

717

.05

405.

8067

0.96

50.

0-0

.075

0.00

10-0

.052

-0.0

060

lm04

63m

8760

82.4

7922

-65.

2473

71.

0594

8317

.87

17.6

819

34.7

227

0.95

6-0

.02

-0.0

40.

0020

-0.0

040

0.00

50lm

0355

k172

1685

.564

42-6

7.06

382

1.06

0366

16.9

916

.83

1248

.615

50.

883

-0.0

45-0

.163

-0.0

2-0

.07

0.0

lm05

51m

9243

76.4

3002

-70.

5058

81.

0646

4916

.53

16.1

918

56.6

163

0.94

6-0

.014

-0.0

64-0

.002

0-0

.016

0.00

20lm

0184

n148

4477

.143

24-6

8.59

311

1.06

7386

17.0

216

.85

2020

.515

10.

968

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11-0

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-0.0

020

-0.0

270.

0lm

0585

m29

810

83.0

6159

-71.

3173

1.06

795

17.2

417

.05

1923

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40.

925

-0.0

23-0

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-0.0

080

-0.0

180.

0030

lm02

90k1

8569

74.0

2612

-66.

3812

91.

0683

9216

.21

16.0

119

25.5

978

0.94

8-0

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-0.0

58-0

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.009

0-0

.002

0lm

0341

n190

184

.046

94-6

6.42

796

1.06

9987

16.7

316

.43

1616

.587

10.

93-0

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-0.1

11-0

.01

-0.0

61-0

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153

lm05

70m

2030

179

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65-7

0.57

244

1.07

0216

16.2

416

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875.

6007

0.93

5-0

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-0.0

82-0

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0-0

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020

lm03

36l2

1294

81.1

102

-67.

5991

61.

0708

4717

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17.5

535

3.83

580.

925

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060

-0.1

390.

0-0

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0030

lm03

34l2

0690

80.8

7888

-67.

2388

71.

0713

3317

.05

16.8

814

95.8

507

0.95

3-0

.101

-0.0

7-0

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-0.0

26-0

.012

lm01

16m

1775

274

.319

9-7

0.21

411

1.07

1932

16.9

016

.68

1608

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00.

859

-0.0

4-0

.188

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19-0

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020

lm01

23m

3222

73.4

2292

-69.

4153

81.

0726

3316

.94

16.8

516

18.5

335

0.93

1-0

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86-0

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0-0

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lm03

35l1

6808

81.8

1014

-67.

2113

21.

0737

0316

.19

15.9

618

67.6

534

0.95

5-0

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0-0

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-0.0

020

-0.0

250.

0lm

0337

k164

4281

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75-6

7.41

741

1.07

405

17.6

117

.48

2463

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30.

963

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090

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61-0

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0-0

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030

lm02

95l1

9334

74.9

3114

-67.

2190

61.

0747

0216

.93

16.7

120

80.9

085

0.97

4-0

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-0.0

24-0

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00.

0010

0.00

10lm

0207

n197

6182

.231

04-6

8.99

163

1.07

4897

17.2

417

.07

2337

.617

50.

943

-0.0

19-0

.097

-0.0

13-0

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0.00

10lm

0335

n642

282

.476

19-6

7.13

888

1.07

6161

17.2

817

.00

802.

8039

0.97

6-0

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27-0

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0-0

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010

lm00

22k2

100

82.1

9138

-69.

4210

81.

0793

8916

.35

16.1

218

81.6

874

0.92

4-0

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82-0

.001

0-0

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0.00

50lm

0184

k200

1576

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47-6

8.47

51.

0797

4117

.45

17.3

612

24.6

259

0.96

5-0

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45-0

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-0.0

27-0

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0lm

0157

n980

372

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28-6

8.92

034

1.08

0202

17.4

317

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429.

7768

0.92

6-0

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15-0

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460.

0030

lm03

14n1

0220

77.8

5657

-67.

1738

51.

0805

6316

.37

16.1

522

34.5

971

0.94

8-0

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0-0

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020

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28-0

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0326

l756

179

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04-6

7.49

735

1.08

1099

16.9

116

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440.

5993

0.97

7-0

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0.00

20-0

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0.00

70lm

0120

n262

0672

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3-6

9.36

574

1.08

1433

16.7

816

.70

1531

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60.

964

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12-0

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-0.0

030

-0.0

21-0

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0lm

0040

k162

2585

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43-6

9.15

902

1.08

7516

17.4

517

.27

1900

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70.

920.

0010

-0.1

0.0

-0.0

42-0

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0lm

0044

m42

0386

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72-6

9.77

792

1.08

7685

16.3

416

.22

1585

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00.

917

-0.0

12-0

.131

-0.0

030

-0.0

77-0

.001

0lm

0311

l247

2578

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42-6

6.56

447

1.09

0105

17.9

217

.74

2234

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10.

9-0

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-0.1

43-0

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-0.0

67-0

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0lm

0374

n604

788

.328

48-6

7.14

495

1.09

0677

17.5

317

.37

1939

.782

70.

97-0

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-0.0

18-0

.002

00.

00.

0060

lm03

01m

2633

676

.876

21-6

6.41

165

1.09

0782

17.8

417

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1438

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80.

971

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3-0

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16-0

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00.

014

lm04

25n2

6027

75.7

4082

-65.

8787

41.

0908

4917

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17.8

216

09.5

550

0.93

70.

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980.

022

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410.

0010

lm05

84l1

1571

81.6

8072

-71.

3754

31.

0919

8917

.78

17.7

718

28.7

310

0.93

4-0

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8-0

.01

-0.0

20.

0030

lm04

66m

1201

981

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79-6

5.98

167

1.09

2537

16.9

216

.69

2142

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80.

972

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1-0

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030

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130.

0020

lm03

43k8

884

83.7

1834

-66.

6522

91.

0926

4416

.74

16.5

417

64.8

820

0.91

1-0

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0-0

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060

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40.

0010

lm05

93l2

4799

84.8

8857

-71.

0928

61.

0933

7517

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17.4

519

15.6

440

0.93

6-0

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0-0

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52-0

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0207

l996

581

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55-6

8.92

461.

0949

0416

.84

16.6

319

66.6

365

0.92

9-0

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0-0

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020

lm03

60n1

1911

86.5

6384

-66.

4813

91.

0951

7917

.76

17.6

419

25.8

028

0.96

6-0

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41-0

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0-0

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020

lm02

07l1

1656

81.6

0031

-68.

9372

91.

0954

1917

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17.7

423

27.6

642

0.98

1-0

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31-0

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-0.0

12-0

.001

0lm

0021

n128

9083

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13-6

9.39

681

1.09

5632

17.4

417

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537.

5088

0.85

6-0

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61-0

.004

0-0

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030

lm03

44m

1045

883

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15-6

7.02

379

1.09

8211

16.2

616

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1300

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40.

992

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1-0

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-0.0

020

-0.0

020

0.00

40lm

0093

n123

5079

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03-6

9.61

813

1.10

0478

17.7

217

.67

1463

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60.

983

-0.0

14-0

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060

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42-0

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0550

k131

3775

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8-7

0.54

11.

1030

217

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16.9

415

91.6

349

0.96

7-0

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550.

0-0

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21l5

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73.2

0473

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2297

31.

1049

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16.0

718

88.5

707

0.94

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050

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83-0

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0-0

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0.0

lm03

66k1

7409

86.0

5265

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427

1.10

5186

16.4

916

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1627

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30.

979

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69-0

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25-0

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64l1

3690

86.2

1409

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2048

91.

1056

1717

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16.8

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79.7

251

0.97

7-0

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47-0

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310.

0030

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43l2

4033

83.4

3983

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9044

51.

1072

9517

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17.0

316

07.6

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66-0

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380.

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46l8

111

82.7

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-67.

5065

51.

1127

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16.9

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0.83

480.

931

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80-0

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0.00

20-0

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0.0

lm02

43l1

6058

88.8

1548

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2634

51.

1128

0717

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17.5

111

16.8

745

0.95

1-0

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0-0

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0.0

lm01

56n2

1172

71.7

8486

-68.

9931

21.

1139

917

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17.5

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03.5

730

0.94

7-0

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73-0

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390.

0040

lm02

83k1

1461

73.2

1344

-66.

6709

61.

1146

2216

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16.8

418

48.7

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0.92

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22-0

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10.

0010

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20

154


0232

l172

5986

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77-6

8.27

398

1.12

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17.3

317

.21

1660

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80.

879

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51-0

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-0.0

26-0

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0.00

40lm

0265

k116

8092

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42-6

8.43

939

1.12

1349

17.6

717

.58

1660

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40.

922

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0-0

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lm04

57k1

8380

80.6

1203

-66.

0282

71.

1273

4717

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17.3

412

57.5

744

0.90

6-0

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28-0

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45-0

.001

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0172

l662

675

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37-6

8.23

722

1.13

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17.1

016

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1848

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895

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415

76.1

4952

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5920

11.

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5216

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16.3

119

56.6

302

0.91

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14-0

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0.00

40lm

0486

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584

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5-6

6.09

065

1.13

1517

17.2

116

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537.

5438

0.94

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75-0

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10k1

5114

77.5

2638

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3516

41.

1329

1817

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17.5

611

47.8

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0.96

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71-0

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34-0

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0690

l244

0077

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16-7

2.17

394

1.13

369

17.3

117

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2124

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80.

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17-0

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150.

0020

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25l2

7285

80.1

7272

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2736

31.

1357

5816

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16.1

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62.6

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10k1

5429

79.7

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1549

61.

1369

3116

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16.5

712

53.5

933

0.96

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35-0

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47l1

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11.

1387

1317

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17.1

421

40.8

425

0.91

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50-0

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0.00

50-0

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0.00

20lm

0292

k211

0174

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71-6

6.77

125

1.13

9525

16.6

316

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2554

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50.

932

0.00

50-0

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33-0

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0556

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867

75.7

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2717

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17.3

648

1.68

310.

967

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12-0

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0214

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682

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61-6

8.56

501

1.14

3016

17.4

417

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1538

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40.

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020

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43-0

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0-0

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0.00

10lm

0245

k790

888

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47-6

8.40

236

1.14

3467

17.5

417

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781.

7629

0.93

3-0

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0-0

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0.00

10-0

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0.00

40lm

0455

l556

780

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19-6

5.73

801

1.14

3775

16.4

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1290

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70.

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40-0

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61n1

8106

78.6

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7047

31.

1438

3916

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16.0

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26.6

240

0.96

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63-0

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17n1

4277

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76-6

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16.3

316

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80.

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39-0

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1-0

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67m

6802

82.5

8253

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9442

31.

1478

0216

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15.8

578

9.69

180.

929

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52-0

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63-0

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0.00

70lm

0417

n935

874

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17-6

6.11

689

1.14

811

17.3

017

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2311

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40.

948

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17-0

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71l2

4463

80.5

5512

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1486

2817

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17.5

511

50.6

653

0.97

3-0

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53-0

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0-0

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0.00

20lm

0031

n172

2485

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1-6

9.37

412

1.14

893

16.5

116

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342.

8286

0.92

8-0

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25l1

2189

85.2

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5813

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1574

2217

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17.2

315

32.6

827

0.97

8-0

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19-0

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00.

0010

0.0

lm00

33m

2670

885

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76-6

9.56

066

1.15

8284

17.1

617

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1997

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30.

982

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18-0

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070

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28-0

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0575

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5380

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22-7

1.43

955

1.16

016

17.3

517

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1819

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40.

965

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14-0

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040

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29-0

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0lm

0014

l200

5480

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12-7

0.03

237

1.16

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17.8

417

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1272

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10.

93-0

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0-0

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0.00

20lm

0466

l192

4281

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84-6

6.19

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1.16

3589

17.4

617

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2016

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20.

975

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16-0

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110.

0020

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83n1

4097

73.3

2353

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8400

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1640

5117

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48.6

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0.92

80.

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35n1

1277

72.4

2784

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4727

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1684

4917

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17.0

315

63.5

932

0.97

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21l1

6803

73.2

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71.

1700

2116

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16.9

212

76.4

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0.98

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020

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21-0

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0lm

0356

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184

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04-6

7.51

859

1.17

3114

17.3

817

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2018

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90.

889

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47-0

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0-0

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0.00

20lm

0103

l139

5177

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49-6

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1.17

4507

16.7

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388.

8527

0.91

2-0

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44-0

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0lm

0226

n241

6884

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96-6

9.02

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16.2

015

.99

1453

.863

70.

944

0.00

90-0

.086

0.00

20-0

.047

-0.0

060

lm04

57l1

9060

80.3

0501

-66.

2145

31.

1761

0817

.40

17.2

214

79.6

849

0.96

1-0

.006

0-0

.052

-0.0

-0.0

340.

0020

lm02

11k1

9128

83.4

5113

-67.

7665

21.

1782

6417

.67

17.3

611

17.6

979

0.94

4-0

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-0.0

79-0

.008

0-0

.042

-0.0

030

lm02

14m

2903

382

.841

72-6

8.52

601

1.17

8663

16.5

416

.60

2072

.458

70.

925

-0.0

040

-0.1

-0.0

040

-0.0

660.

0050

lm05

40l2

2424

72.8

5002

-70.

7602

91.

1818

8117

.14

16.9

914

64.6

401

0.92

1-0

.002

0-0

.12

0.00

10-0

.07

0.0

lm03

03l2

3428

76.8

0088

-66.

8860

91.

1836

6917

.71

17.6

113

83.8

448

0.88

3-0

.054

-0.1

63-0

.025

-0.0

670.

0030

lm00

21k2

2831

82.8

9536

-69.

1894

11.

1845

3917

.05

17.0

393

1.47

170.

967

0.00

50-0

.062

0.00

30-0

.036

-0.0

030

lm02

01k1

0778

81.5

9068

-67.

7074

1.18

7596

17.7

417

.71

780.

8087

0.97

-0.0

090

-0.0

4-0

.002

0-0

.03

-0.0

010

lm03

12k1

5523

77.4

8035

-66.

7319

41.

1881

1717

.51

17.5

217

64.8

517

0.95

6-0

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-0.0

51-0

.007

0-0

.012

-0.0

155

lm01

14m

2789

974

.302

06-6

9.91

214

1.19

1167

16.8

916

.81

2009

.540

90.

942

0.00

20-0

.078

-0.0

030

-0.0

480.

0020

lm02

00k1

9885

80.4

2683

-67.

8309

21.

1914

8317

.40

17.4

121

93.7

733

0.94

-0.0

32-0

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-0.0

040

-0.0

14-0

.005

0lm

0120

n612

472

.418

07-6

9.23

849

1.19

1658

16.4

716

.31

1071

.742

70.

958

-0.0

12-0

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-0.0

-0.0

050

0.0

lm03

66k1

0436

86.2

3861

-67.

3747

41.

1933

4616

.52

16.2

819

41.7

860

0.91

4-0

.012

-0.1

53-0

.01

-0.0

87-0

.003

0lm

0165

m30

398

74.7

6377

-68.

5201

61.

1936

417

.37

17.0

844

2.81

820.

965

-0.0

14-0

.044

-0.0

070

-0.0

240.

0050

lm00

44k3

974

86.1

2024

-69.

7789

31.

1936

816

.19

16.0

919

41.6

268

0.96

1-0

.013

-0.0

46-0

.002

0-0

.003

00.

0lm

0344

m18

5083

.064

17-6

6.96

759

1.19

3709

16.3

016

.11

1129

.748

10.

946

-0.0

060

-0.0

65-0

.003

0-0

.038

0.00

10lm

0121

k249

2272

.807

62-6

9.22

294

1.19

5194

15.9

015

.79

1281

.514

90.

941

-0.0

17-0

.061

-0.0

040

-0.0

12-0

.002

0lm

0471

m36

3184

.126

83-6

5.00

347

1.19

5592

17.6

817

.44

1751

.924

40.

862

-0.0

52-0

.127

-0.0

090

-0.0

050

0.01

3lm

0210

n255

6883

.094

13-6

7.96

484

1.19

6126

17.3

217

.12

2000

.563

80.

961

-0.0

24-0

.043

-0.0

020

-0.0

050

0.00

30lm

0193

l102

6279

.739

84-6

8.21

21.

2009

917

.30

17.1

117

50.8

674

0.97

1-0

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-0.0

59-0

.02

-0.0

440.

0070

lm01

23m

1977

973

.332

47-6

9.51

175

1.20

2701

17.1

117

.13

2187

.649

20.

978

-0.0

12-0

.045

-0.0

080

-0.0

28-0

.0lm

0214

n253

9382

.796

08-6

8.66

299

1.20

5505

17.3

817

.37

494.

5888

0.96

9-0

.01

-0.0

51-0

.001

0-0

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-0.0

010

lm01

00m

7540

76.2

7001

-69.

0982

61.

2062

1717

.43

17.3

320

03.5

390

0.93

6-0

.041

-0.0

97-0

.013

-0.0

31-0

.006

0lm

0115

n144

6375

.733

43-6

9.98

184

1.20

6817

.13

16.9

419

62.6

879

0.95

9-0

.007

0-0

.071

0.00

20-0

.034

0.0

lm02

90m

1223

674

.277

58-6

6.33

021

1.20

6866

16.8

016

.84

949.

4763

0.96

6-0

.017

-0.0

45-0

.002

0-0

.017

0.00

10lm

0286

l230

8172

.098

21-6

7.61

777

1.20

7038

17.4

917

.21

1899

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90.

879

-0.0

42-0

.125

-0.0

16-0

.048

0.0

lm03

73m

2039

589

.298

-66.

7384

91.

2076

7217

.88

17.7

716

06.6

476

0.93

6-0

.043

-0.0

88-0

.016

-0.0

2-0

.001

0lm

0230

m92

5986

.430

74-6

7.71

334

1.20

7767

17.6

717

.49

1620

.674

00.

871

-0.0

6-0

.16

-0.0

2-0

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-0.0

010

lm01

93n5

944

80.2

5679

-68.

1829

31.

2077

7517

.54

17.4

519

29.6

674

0.86

7-0

.054

-0.1

69-0

.021

-0.0

68-0

.0lm

0316

k135

9777

.610

99-6

7.39

053

1.20

9809

16.4

816

.25

1874

.623

50.

981

-0.0

080

-0.0

16-0

.001

0-0

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0010

lm05

40k2

2686

72.9

5889

-70.

6023

81.

2107

0817

.84

17.6

416

27.5

133

0.98

-0.0

17-0

.046

-0.0

090

-0.0

350.

0010

lm03

02n1

2595

76.3

274

-66.

8322

31.

2131

5117

.18

16.8

915

31.6

134

0.92

6-0

.01

-0.0

3-0

.002

0-0

.017

0.00

90lm

0030

n681

584

.470

05-6

9.39

718

1.21

3239

16.4

016

.27

818.

8345

0.93

7-0

.025

-0.0

71-0

.006

0-0

.015

0.00

30lm

0167

l208

7974

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04-6

9.00

567

1.21

3472

17.0

516

.83

760.

7172

0.93

7-0

.005

0-0

.117

-0.0

030

-0.0

73-0

.002

0lm

0290

m76

5174

.332

92-6

6.29

643

1.21

3756

17.4

617

.64

459.

7105

0.89

6-0

.003

0-0

.14

-0.0

010

-0.0

73-0

.003

0lm

0255

m21

132

91.1

7064

-68.

5159

21.

2139

9417

.74

17.5

718

28.8

639

0.89

9-0

.002

0-0

.132

-0.0

010

-0.0

69-0

.001

0lm

0352

l241

1284

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5-6

6.92

691

1.21

4317

17.6

317

.43

1812

.767

90.

901

-0.0

010

-0.1

40.

0020

-0.0

630.

0040

lm00

33l8

069

84.9

8061

-69.

6016

81.

2150

3916

.80

16.9

118

83.7

074

0.94

9-0

.011

-0.0

71-0

.004

0-0

.038

0.00

40lm

0423

m21

313

75.7

7782

-65.

3418

41.

2157

417

.68

17.5

212

79.5

999

0.97

40.

03-0

.006

0-0

.006

00.

0090

0.02

4lm

0553

l264

2775

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62-7

1.10

917

1.21

6011

16.2

316

.11

1284

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00.

952

-0.0

15-0

.045

-0.0

010

-0.0

0.00

10lm

0240

l139

4087

.988

11-6

7.89

771

1.22

005

17.3

817

.26

2256

.649

50.

984

-0.0

28-0

.023

-0.0

070

-0.0

11-0

.002

0lm

0352

l116

3484

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92-6

6.83

952

1.22

1534

17.6

417

.46

2346

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00.

955

-0.0

19-0

.047

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070

-0.0

14-0

.001

0lm

0343

m24

594

84.0

397

-66.

7512

71.

2220

6317

.60

17.4

217

74.9

006

0.95

6-0

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36-0

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0-0

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00.

0010

lm03

43l2

7142

83.7

4179

-66.

9221

11.

2243

617

.46

17.3

412

71.5

780

0.95

50.

0080

-0.0

630.

0020

-0.0

28-0

.001

0lm

0552

n281

0275

.408

52-7

1.12

939

1.22

4882

17.6

117

.44

1836

.681

00.

973

-0.0

12-0

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-0.0

060

-0.0

34-0

.004

0lm

0025

l199

4083

.133

71-7

0.01

572

1.22

5202

17.6

417

.61

1305

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70.

976

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18-0

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070

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170.

0050

lm03

46l1

3640

82.5

6262

-67.

5497

91.

2253

1616

.41

16.1

719

53.7

492

0.93

5-0

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0-0

.113

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060

-0.0

59-0

.002

0lm

0200

l205

6180

.503

97-6

7.94

531.

2258

5216

.01

15.7

912

59.5

936

0.93

5-0

.02

-0.0

81-0

.009

0-0

.03

0.00

40lm

0191

k123

0679

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-67.

7135

11.

2260

2417

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17.0

682

8.67

581.

006

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28-0

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-0.0

040

-0.0

39-0

.007

0lm

0184

n225

6377

.173

64-6

8.63

574

1.22

6475

17.4

517

.30

2185

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20.

929

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45-0

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42-0

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0

156


0304

n298

4276

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02-6

7.29

102

1.22

9024

16.6

416

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1476

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90.

902

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16-0

.148

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090

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870.

0060

lm01

00l2

2131

75.9

6004

-69.

3549

31.

2293

7117

.53

17.4

019

45.6

895

0.89

4-0

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45-0

.023

-0.0

64-0

.0lm

0452

m16

067

79.9

2772

-65.

338

1.22

9623

16.5

016

.31

826.

7593

0.94

9-0

.015

-0.0

53-0

.002

0-0

.003

00.

0030

lm03

44m

8364

83.3

4386

-67.

0099

1.23

1791

17.6

617

.58

1184

.691

30.

96-0

.018

-0.0

58-0

.013

-0.0

39-0

.001

0lm

0347

k206

2883

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59-6

7.44

287

1.23

1871

16.5

716

.38

2255

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10.

992

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040

-0.0

12-0

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00.

0010

lm00

90m

2646

678

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57-6

9.20

741

1.23

2396

17.2

316

.97

1881

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60.

877

0.00

10-0

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030

-0.0

960.

0010

lm02

52l2

2660

90.1

5279

-68.

3259

91.

2336

3817

.15

16.9

783

5.81

100.

877

-0.0

070

-0.1

82-0

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0-0

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0.00

80lm

0336

m21

470

81.5

9424

-67.

4457

61.

2360

9617

.43

17.2

219

74.6

066

0.94

4-0

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-0.0

9-0

.005

0-0

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0.00

70lm

0343

m18

540

84.1

7664

-66.

7115

21.

2373

3616

.56

16.2

519

40.7

662

0.95

1-0

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0-0

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020

-0.0

51-0

.004

0lm

0157

n721

772

.681

38-6

8.89

908

1.23

7435

16.3

916

.15

435.

8342

0.89

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26-0

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1-0

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030

lm02

22n4

768

84.5

9285

-68.

1869

91.

2383

9217

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17.1

215

78.6

544

0.92

40.

011

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270.

0070

-0.0

74-0

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0lm

0344

l595

982

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7-6

7.14

957

1.24

0057

17.3

017

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1187

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90.

947

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010

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07-0

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0-0

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040

lm00

90m

1364

778

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54-6

9.13

381

1.24

0532

16.8

716

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1503

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30.

922

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050

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23-0

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0-0

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020

lm00

95l3

2222

78.8

8433

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41.

2428

4917

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17.6

112

24.6

295

0.94

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680.

0050

lm01

10l8

980

73.8

8764

-69.

2616

91.

2440

616

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16.5

412

10.6

036

0.89

8-0

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49-0

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0-0

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0.00

60lm

0175

m17

458

76.5

3673

-68.

4479

11.

2448

9716

.47

16.2

211

50.6

119

0.95

3-0

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53-0

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0-0

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lm03

03n1

0523

77.2

0164

-66.

8071

21.

2463

2117

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17.6

519

36.6

491

0.90

7-0

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0-0

.143

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050

-0.0

45-0

.0lm

0276

k139

8293

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65-6

8.80

429

1.24

7657

17.1

516

.93

1786

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70.

855

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49-0

.145

-0.0

2-0

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0.00

20lm

0294

l782

574

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49-6

7.15

764

1.24

8422

16.5

316

.33

1775

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30.

969

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16-0

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0.00

200.

0010

0.00

20lm

0342

n240

0282

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53-6

6.92

396

1.24

847

17.4

917

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1114

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30.

984

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4-0

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22-0

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-0.0

020

lm05

51n1

8330

76.5

7531

-70.

7105

41.

2491

2716

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16.2

817

61.8

763

0.96

40.

0030

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550.

0010

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360.

0070

lm03

43n2

5612

83.8

4745

-66.

9110

21.

2496

5317

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17.2

479

2.75

700.

991

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21-0

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070

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120.

0020

lm03

04n2

4921

75.9

9117

-67.

2605

61.

2499

8516

.56

16.2

916

28.5

280

0.96

3-0

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0-0

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0.0

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320.

0030

lm02

14n7

884

82.8

0062

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5543

91.

2503

0517

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16.8

819

37.7

049

0.92

7-0

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05-0

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0-0

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0.01

lm00

44l2

4715

85.9

8352

-70.

0618

51.

2514

6317

.73

17.7

713

88.8

593

0.94

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3-0

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-0.0

11-0

.01

0.01

1lm

0322

m43

8679

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01-6

6.62

687

1.25

4285

17.8

317

.68

2018

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00.

989

-0.0

37-0

.017

-0.0

17-0

.014

0.00

50lm

0020

m14

007

82.4

4224

-69.

1412

81.

2565

1816

.99

17.1

514

48.7

009

0.93

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060

-0.0

86-0

.006

0-0

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0.00

20lm

0182

l131

9176

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15-6

8.23

504

1.25

6523

17.1

416

.88

2198

.654

70.

871

-0.0

48-0

.19

-0.0

31-0

.09

-0.0

020

lm02

90m

1911

174

.205

15-6

6.38

201

1.25

7556

16.1

415

.85

2199

.797

60.

971

-0.0

15-0

.04

-0.0

040

-0.0

150.

0010

lm03

25m

1576

880

.752

34-6

7.04

384

1.26

0551

16.8

916

.59

434.

7552

0.97

1-0

.014

-0.0

280.

0020

0.00

10-0

.002

0lm

0283

m24

518

73.5

2331

-66.

7657

1.26

0717

16.1

715

.93

1777

.773

90.

935

-0.0

25-0

.094

-0.0

090

-0.0

570.

0020

lm00

54l5

210

87.7

6585

-69.

9396

11.

2618

3616

.38

16.1

813

17.5

507

0.95

1-0

.018

-0.0

6-0

.006

0-0

.017

0.00

30lm

0343

l259

1283

.711

14-6

6.91

478

1.26

4852

16.0

315

.85

1266

.609

40.

985

-0.0

16-0

.024

-0.0

060

-0.0

110.

0lm

0110

l132

8873

.852

5-6

9.29

033

1.27

1404

16.1

715

.96

1306

.500

30.

972

-0.0

2-0

.052

-0.0

060

-0.0

31-0

.0lm

0671

l505

674

.580

04-7

2.12

418

1.27

1916

17.8

317

.76

1856

.608

30.

969

-0.0

39-0

.057

-0.0

19-0

.036

0.00

30lm

0253

l835

590

.851

1-6

8.34

826

1.27

4284

17.4

717

.39

1759

.902

20.

935

-0.0

51-0

.088

-0.0

18-0

.032

-0.0

050

lm04

36k8

952

76.3

6602

-65.

9675

41.

2755

9617

.75

17.6

020

21.5

603

0.99

-0.0

59-0

.02

-0.0

12-0

.005

0-0

.01

lm02

14m

2985

882

.792

06-6

8.53

141

1.27

9218

17.3

617

.35

2008

.563

90.

953

-0.0

080

-0.0

66-0

.003

0-0

.042

0.00

20lm

0555

m12

064

76.7

5923

-71.

2361

51.

2798

4816

.15

15.8

621

86.6

970

0.88

-0.0

17-0

.073

-0.0

030

-0.0

130.

0050

lm05

83m

2571

282

.933

24-7

0.93

984

1.28

0423

17.0

517

.09

2183

.776

20.

951

-0.0

26-0

.06

-0.0

11-0

.026

0.00

40lm

0595

n912

685

.454

16-7

1.35

427

1.28

2031

16.3

116

.18

1388

.856

00.

984

-0.0

020

-0.0

34-0

.002

0-0

.02

0.0

157

lm00

50l9

127

88.1

6042

-69.

2585

81.

2830

1517

.94

17.7

618

62.7

808

0.95

1-0

.049

-0.1

1-0

.014

-0.0

5-0

.003

0lm

0012

m20

602

80.6

4068

-69.

5489

81.

2841

0117

.65

17.2

911

38.8

386

0.94

1-0

.002

0-0

.146

-0.0

030

-0.0

94-0

.003

0lm

0197

n195

3480

.181

87-6

8.98

964

1.28

4845

17.6

217

.26

1933

.738

00.

896

0.00

30-0

.188

0.00

60-0

.101

-0.0

070

lm03

54l1

7529

84.6

4993

-67.

2259

1.28

8998

17.9

417

.82

1181

.793

50.

906

-0.0

76-0

.162

-0.0

38-0

.081

0.00

10lm

0017

m17

883

81.7

5557

-70.

2145

71.

2899

6717

.21

17.3

014

80.8

179

0.98

2-0

.016

-0.0

31-0

.006

0-0

.012

0.00

20lm

0343

k105

3983

.439

29-6

6.66

403

1.29

1479

17.8

117

.75

1597

.662

20.

902

-0.0

27-0

.09

-0.0

12-0

.007

00.

0030

lm02

93l1

4089

74.9

9618

-66.

8347

81.

2920

417

.72

17.5

418

42.8

031

0.98

10.

0050

-0.0

260.

0-0

.019

-0.0

010

lm00

30k6

634

84.0

2922

-69.

0985

1.29

3848

16.1

816

.06

1808

.853

50.

879

-0.0

3-0

.137

-0.0

080

-0.0

440.

0010

lm03

66k1

9655

86.1

4187

-67.

4436

31.

2954

7116

.85

16.6

714

43.7

901

0.86

7-0

.058

-0.1

83-0

.036

-0.0

90.

0050

lm03

51m

7030

85.9

5719

-66.

2857

21.

2961

5316

.49

16.2

755

6.59

730.

976

0.00

10-0

.038

-0.0

020

-0.0

250.

0010

lm01

84k1

1257

76.9

6216

-68.

4233

91.

2978

7516

.95

16.8

414

55.7

438

0.97

8-0

.012

-0.0

22-0

.007

0-0

.013

0.00

10lm

0134

m16

531

70.3

6211

-69.

8530

91.

2984

1616

.83

16.7

518

74.5

483

0.96

6-0

.015

-0.0

35-0

.002

00.

0010

-0.0

030

lm02

20n2

0494

84.7

732

-67.

9360

21.

2991

8317

.16

17.0

112

62.5

922

0.94

6-0

.022

-0.0

6-0

.005

0-0

.007

00.

0040

lm03

45k2

244

83.6

8146

-66.

9685

81.

3010

8516

.48

16.3

315

11.7

218

0.94

6-0

.016

-0.0

8-0

.009

0-0

.039

-0.0

030

lm02

07l9

702

81.6

2493

-68.

9232

81.

3027

5316

.36

16.2

914

44.7

445

0.97

-0.0

11-0

.038

-0.0

040

-0.0

2-0

.004

0lm

0200

l209

5280

.520

18-6

7.94

839

1.30

4803

16.3

916

.16

2029

.486

70.

917

-0.0

22-0

.122

-0.0

070

-0.0

64-0

.002

0lm

0313

k266

2278

.360

45-6

6.75

854

1.30

5016

17.4

417

.29

2310

.659

60.

934

-0.0

050

-0.1

29-0

.003

0-0

.09

0.00

20lm

0122

n218

0972

.586

73-6

9.70

246

1.30

534

16.4

916

.25

2356

.561

90.

946

0.00

20-0

.077

0.00

10-0

.038

-0.0

lm00

33k1

6643

84.8

3539

-69.

5019

41.

3057

4315

.79

15.7

316

29.6

272

0.94

5-0

.024

-0.0

82-0

.009

0-0

.044

0.0

lm00

33k2

8357

84.9

2359

-69.

5735

41.

3068

4115

.88

15.7

723

50.6

233

0.88

1-0

.017

-0.1

51-0

.009

0-0

.066

0.00

20lm

0313

k253

7178

.469

32-6

6.75

051.

3073

0617

.71

17.6

053

9.53

050.

955

0.00

20-0

.076

-0.0

-0.0

550.

0010

lm02

21m

2641

885

.521

84-6

7.81

625

1.30

898

17.4

517

.34

1538

.683

40.

941

0.00

20-0

.07

-0.0

040

-0.0

43-0

.001

0lm

0632

l197

3692

.18

-71.

1302

31.

3097

716

.95

16.7

914

93.8

556

0.92

5-0

.038

-0.1

04-0

.013

-0.0

53-0

.0lm

0344

k452

582

.802

74-6

6.98

583

1.31

0804

16.6

816

.51

802.

8137

0.93

9-0

.015

-0.0

81-0

.008

0-0

.041

-0.0

010

lm03

45k7

107

83.7

232

-67.

0005

61.

3110

4216

.12

15.9

111

52.8

469

0.94

4-0

.003

0-0

.09

0.00

20-0

.046

-0.0

040

lm01

90n1

4623

79.1

1976

-67.

8913

81.

3116

5715

.87

15.6

311

95.6

954

0.84

7-0

.02

-0.2

05-0

.008

0-0

.071

-0.0

lm03

44m

5728

83.1

9564

-66.

9930

31.

3127

9317

.08

16.9

048

9.63

830.

932

-0.0

070

-0.1

150.

0020

-0.0

770.

0010

lm05

51m

1650

476

.628

32-7

0.55

247

1.31

4528

16.6

416

.27

423.

6287

0.94

4-0

.025

-0.0

79-0

.012

-0.0

40.

0020

lm05

70l6

310

79.1

5194

-70.

6397

41.

3147

3717

.66

17.5

018

70.6

559

0.93

7-0

.004

0-0

.064

-0.0

060

-0.0

43-0

.001

0lm

0323

l773

880

.259

7-6

6.79

721.

3152

2416

.99

16.8

913

04.4

933

0.98

4-0

.011

-0.0

43-0

.002

0-0

.036

0.0

lm05

95m

2515

485

.297

65-7

1.29

029

1.31

7016

17.5

917

.74

2227

.659

60.

972

-0.0

020

-0.0

67-0

.002

0-0

.046

0.00

20lm

0321

m13

358

80.3

4625

-66.

3294

71.

3182

117

.46

17.1

619

59.6

417

0.93

5-0

.005

0-0

.1-0

.002

0-0

.05

0.00

10lm

0551

k190

7876

.015

96-7

0.59

653

1.31

8882

17.3

417

.16

1278

.541

50.

978

-0.0

17-0

.026

-0.0

060

-0.0

11-0

.001

0lm

0466

m23

585

81.4

4584

-66.

0769

41.

3189

5816

.68

16.5

122

50.6

023

0.90

4-0

.039

-0.1

42-0

.012

-0.0

51-0

.001

0lm

0340

n223

8383

.092

96-6

6.55

266

1.31

9689

17.7

617

.62

1476

.741

70.

934

-0.0

040

-0.0

78-0

.002

0-0

.037

0.00

20lm

0366

n145

9386

.898

47-6

7.55

653

1.32

1337

17.7

817

.55

450.

8444

0.93

-0.0

17-0

.091

-0.0

050

-0.0

51-0

.003

0lm

0032

k203

1384

.144

94-6

9.56

391.

3237

9217

.14

17.0

780

2.76

030.

97-0

.004

0-0

.063

-0.0

070

-0.0

510.

0lm

0012

l179

3579

.963

02-6

9.66

736

1.32

3984

16.5

916

.44

1622

.552

10.

929

-0.0

030

-0.1

06-0

.006

0-0

.051

0.00

10lm

0210

m22

011

83.1

1026

-67.

7938

71.

3249

5617

.02

16.8

611

79.7

954

0.87

-0.0

56-0

.184

-0.0

27-0

.079

0.00

10lm

0033

m68

5085

.370

87-6

9.44

069

1.32

799

17.1

717

.03

2009

.524

80.

933

-0.0

090

-0.1

05-0

.005

0-0

.07

0.00

10lm

0343

l597

7*83

.647

48-6

6.79

113

1.32

9154

15.8

215

.64

760.

6928

0.96

5-0

.014

-0.0

39-0

.001

0-0

.007

00.

0010

158


0175

n261

0776

.527

85-6

8.64

711

1.32

9774

17.5

617

.07

1866

.592

60.

972

0.00

60-0

.078

-0.0

070

-0.0

43-0

.002

0lm

0330

l180

2181

.082

09-6

6.52

792

1.33

0011

16.5

416

.42

1219

.645

90.

962

0.00

40-0

.052

0.00

10-0

.023

0.0

lm03

64l6

843

86.3

1096

-67.

1538

51.

3313

7516

.87

16.6

911

50.7

712

0.89

9-0

.039

-0.1

27-0

.013

-0.0

420.

0070

lm03

24n1

1221

79.5

0773

-67.

1743

91.

3342

2716

.89

16.7

718

42.8

412

0.99

5-0

.025

-0.0

030

-0.0

060

-0.0

020

0.00

20lm

0701

k237

7981

.551

07-7

1.99

519

1.33

4253

17.0

216

.86

1496

.681

30.

962

-0.0

010

-0.0

650.

0-0

.046

-0.0

010

lm01

75k1

8907

75.8

0158

-68.

4579

1.33

5629

16.0

215

.96

1447

.754

50.

98-0

.004

0-0

.02

-0.0

030

-0.0

050

0.00

40lm

0110

m24

838

74.6

0204

-69.

1989

81.

3374

5816

.65

16.1

111

98.6

206

0.88

1-0

.043

-0.1

61-0

.016

-0.0

740.

0030

lm02

10k2

4451

82.3

372

-67.

8214

81.

3374

6816

.71

16.5

323

24.6

279

0.89

8-0

.02

-0.1

08-0

.008

0-0

.033

0.00

10lm

0587

n193

8582

.931

65-7

1.78

783

1.33

9509

16.7

216

.65

792.

6937

0.93

9-0

.032

-0.0

94-0

.011

-0.0

450.

0lm

0056

n227

3588

.608

05-7

0.40

959

1.34

1028

16.8

316

.65

2240

.855

60.

941

0.00

50-0

.09

0.0

-0.0

47-0

.001

0lm

0012

l193

9680

.177

63-6

9.67

576

1.34

2001

16.5

816

.17

1528

.660

40.

923

-0.0

2-0

.082

-0.0

040

-0.0

180.

0010

lm00

45n2

7451

87.4

8414

-70.

0613

21.

3427

316

.22

15.9

014

78.7

717

0.95

4-0

.021

-0.0

67-0

.013

-0.0

37-0

.004

0lm

0125

m17

447

73.7

3964

-69.

8470

91.

3430

6117

.76

17.6

821

84.6

421

0.92

6-0

.046

-0.0

91-0

.012

-0.0

39-0

.001

0lm

0032

m19

079

84.2

3338

-69.

5523

51.

3442

1416

.41

16.2

583

3.79

560.

952

-0.0

080

-0.0

57-0

.004

0-0

.022

-0.0

010

lm00

90k1

5522

77.8

3539

-69.

1541

51.

3452

3917

.16

17.3

359

6.46

830.

931

-0.0

090

-0.0

98-0

.005

0-0

.058

-0.0

lm04

24k1

2950

74.7

7183

-65.

6399

31.

3454

9816

.39

16.1

921

84.6

886

0.97

9-0

.01

-0.0

21-0

.005

0-0

.007

00.

0010

lm05

57n1

6353

76.7

8602

-71.

7722

81.

3469

9617

.01

16.8

011

96.5

924

0.93

1-0

.026

-0.0

82-0

.007

0-0

.017

0.00

20lm

0091

l131

4179

.184

65-6

9.27

812

1.34

7207

16.9

116

.91

1903

.589

90.

925

-0.0

1-0

.1-0

.009

0-0

.052

-0.0

010

lm00

40k2

5840

85.8

8344

-69.

2279

51.

3528

1917

.77

17.6

022

28.8

571

0.94

5-0

.016

-0.0

99-0

.008

0-0

.062

-0.0

010

lm00

95n2

1786

79.3

5908

-70.

0243

1.35

5226

17.3

917

.34

2263

.645

90.

883

-0.0

48-0

.141

-0.0

23-0

.046

-0.0

030

lm00

33l1

2538

85.1

8187

-69.

6284

81.

3562

6117

.03

17.1

066

3.93

310.

977

-0.0

010

-0.0

41-0

.001

0-0

.031

-0.0

010

lm01

62l1

1792

73.1

5868

-68.

2297

11.

3563

8317

.47

17.4

217

63.7

818

0.97

7-0

.014

-0.0

35-0

.009

0-0

.009

00.

0lm

0020

m26

7582

.414

69-6

9.06

903

1.35

6457

17.2

117

.00

1439

.776

80.

932

-0.0

040

-0.1

310.

0010

-0.0

88-0

.004

0lm

0225

k231

6685

.099

11-6

8.49

51.

3575

1916

.52

16.3

912

11.7

171

0.87

1-0

.002

0-0

.167

-0.0

010

-0.0

560.

0020

lm05

41n1

0909

74.4

1288

-70.

6943

41.

3578

1817

.91

17.7

014

76.6

226

0.96

8-0

.013

-0.0

5-0

.008

0-0

.038

0.00

10lm

0122

n147

3072

.596

75-6

9.65

419

1.35

9095

17.4

417

.26

2227

.564

50.

971

-0.0

18-0

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0.00

10-0

.004

00.

0020

lm00

33l2

0481

85.1

2016

-69.

6773

41.

3599

6117

.11

17.2

818

88.7

095

0.94

8-0

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-0.0

46-0

.002

0-0

.008

00.

0020

lm02

25m

4465

85.9

3241

-68.

3747

81.

3606

3416

.37

16.1

519

52.6

404

0.95

8-0

.001

0-0

.073

-0.0

070

-0.0

46-0

.002

0lm

0325

k818

480

.162

87-6

7.00

164

1.36

1238

16.2

516

.09

2223

.829

50.

959

-0.0

12-0

.044

-0.0

010

-0.0

090

0.00

10lm

0164

n109

4373

.532

5-6

8.57

395

1.36

2005

16.5

816

.38

1851

.586

80.

972

-0.0

29-0

.035

-0.0

070

-0.0

170.

0020

lm03

06m

1121

876

.160

53-6

7.36

918

1.36

289

16.8

716

.65

2233

.825

80.

935

-0.0

17-0

.071

-0.0

050

-0.0

17-0

.0lm

0167

n661

974

.392

94-6

8.90

038

1.36

3124

17.5

017

.26

434.

7245

0.93

5-0

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0-0

.077

0.00

30-0

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-0.0

050

lm03

31n1

1495

82.3

3892

-66.

5626

61.

3631

6515

.84

15.5

421

68.7

479

0.85

6-0

.037

-0.1

86-0

.012

-0.0

660.

0lm

0055

m20

627

89.4

7672

-69.

8823

61.

3653

1217

.43

17.2

620

20.6

020

0.97

8-0

.02

-0.0

22-0

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0-0

.001

00.

0010

lm03

26k1

5236

79.2

7837

-67.

3988

81.

3657

0217

.77

17.7

222

36.5

552

0.96

4-0

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-0.0

240.

0010

-0.0

020

0.01

1lm

0292

k470

574

.026

2-6

6.63

217

1.36

6304

17.6

717

.53

1973

.570

20.

956

-0.0

12-0

.06

-0.0

060

-0.0

42-0

.0lm

0610

k122

888

.045

73-7

0.49

025

1.36

879

17.4

817

.34

452.

7291

0.97

6-0

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-0.0

23-0

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.008

00.

0050

lm05

51k2

1201

76.1

7855

-70.

6123

61.

3703

515

.97

15.7

417

69.8

058

0.95

20.

0010

-0.0

60.

0040

-0.0

250.

0010

lm02

16l7

335

82.6

3094

-68.

9099

61.

3703

6717

.28

17.1

815

47.6

934

0.93

9-0

.025

-0.0

64-0

.003

0-0

.015

-0.0

lm03

31l1

2991

81.6

9989

-66.

4870

71.

3704

9217

.56

17.4

217

74.8

883

0.92

7-0

.044

-0.1

08-0

.019

-0.0

46-0

.002

0lm

0587

k638

782

.401

28-7

1.54

306

1.37

2249

17.0

016

.78

1761

.886

50.

985

-0.0

15-0

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0.0

-0.0

060

-0.0

020

159

lm05

84k1

4035

81.3

1538

-71.

2356

81.

3727

7716

.40

16.2

467

0.89

050.

966

-0.0

24-0

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-0.0

040

-0.0

120.

0030

lm04

26m

6757

75.1

0942

-65.

9426

61.

3727

8516

.54

16.3

232

5.91

020.

99-0

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-0.0

16-0

.004

0-0

.013

0.00

10lm

0194

l205

1278

.556

26-6

8.63

336

1.37

3732

16.9

216

.76

2009

.550

60.

977

-0.0

2-0

.036

-0.0

060

-0.0

130.

0040

lm04

85l1

6305

85.5

1608

-65.

8128

61.

3740

2117

.56

17.3

913

98.8

692

0.88

9-0

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-0.1

67-0

.022

-0.0

8-0

.0lm

0031

n122

8285

.262

32-6

9.38

275

1.37

5196

16.1

416

.07

1498

.711

20.

901

-0.0

060

-0.1

24-0

.001

0-0

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-0.0

010

lm02

95k2

7975

74.8

5443

-67.

1197

21.

3754

8316

.96

16.8

311

47.7

847

0.87

6-0

.034

-0.1

16-0

.008

0-0

.044

0.00

40lm

0575

n394

780

.715

9-7

1.35

661

1.37

5523

16.4

016

.19

825.

8252

0.97

5-0

.006

0-0

.036

-0.0

040

-0.0

23-0

.002

0lm

0186

n256

9977

.465

51-6

9.03

439

1.37

6787

16.9

416

.72

2187

.721

50.

856

-0.0

43-0

.156

-0.0

19-0

.048

0.00

10lm

0285

k397

273

.072

18-6

6.97

331.

3774

8616

.90

16.9

021

30.7

948

0.98

-0.0

11-0

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-0.0

040

-0.0

20.

0lm

0315

n682

178

.881

15-6

7.13

714

1.37

8079

17.0

216

.75

2240

.805

20.

979

0.00

30-0

.033

0.00

20-0

.013

0.00

10lm

0601

l272

3486

.711

28-7

0.76

364

1.37

8285

17.7

617

.72

1388

.863

00.

907

-0.0

63-0

.123

-0.0

28-0

.062

0.00

50lm

0010

n998

180

.637

01-6

9.27

116

1.37

9098

16.8

616

.61

2202

.685

50.

979

-0.0

13-0

.034

-0.0

010

-0.0

050

0.00

50lm

0123

k255

5073

.257

35-6

9.54

389

1.37

9496

17.7

517

.75

424.

8026

0.94

5-0

.005

0-0

.083

-0.0

020

-0.0

57-0

.002

0lm

0010

k356

379

.888

56-6

9.07

681

1.38

0453

17.5

317

.36

1306

.539

30.

866

-0.0

55-0

.132

-0.0

030

-0.0

060

0.01

6lm

0161

l222

5374

.140

08-6

7.93

355

1.38

0684

17.2

917

.12

1755

.906

80.

946

0.00

60-0

.073

0.00

20-0

.024

-0.0

040

lm00

33k1

6425

84.8

1241

-69.

5006

71.

3818

4115

.95

15.8

415

49.7

162

0.92

8-0

.003

0-0

.104

0.00

30-0

.064

-0.0

030

lm01

87k2

5395

77.8

1155

-68.

8599

61.

3844

7616

.89

16.8

988

4.57

970.

943

-0.0

050

-0.0

91-0

.003

0-0

.038

0.00

10lm

0033

l898

285

.159

85-6

9.60

625

1.38

4664

17.4

617

.36

2347

.595

70.

959

-0.0

090

-0.0

74-0

.003

0-0

.056

-0.0

020

lm01

21n1

0952

73.6

4131

-69.

2638

11.

3896

3116

.94

16.7

715

03.6

168

0.96

3-0

.01

-0.0

34-0

.007

0-0

.017

-0.0

010

lm00

37n1

5636

85.4

7739

-70.

3667

81.

3899

8717

.71

17.6

314

65.7

833

0.93

6-0

.04

-0.1

1-0

.008

0-0

.038

-0.0

070

lm04

53n1

8119

80.8

885

-65.

4649

81.

3924

8717

.53

17.4

021

60.7

252

1.00

6-0

.027

-0.0

050

-0.0

040

-0.0

030

0.00

40lm

0346

m15

709

83.1

288

-67.

4078

11.

3961

6415

.72

15.5

319

10.7

349

0.99

3-0

.019

-0.0

060

-0.0

050

-0.0

020

0.00

40lm

0337

k241

8781

.788

41-6

7.47

141.

3972

2716

.60

16.3

920

20.5

398

0.98

-0.0

11-0

.04

-0.0

070

-0.0

170.

0020

lm02

17n1

2376

83.9

6639

-68.

9427

91.

3981

9816

.30

16.0

823

27.6

841

0.98

9-0

.008

0-0

.011

-0.0

-0.0

020

0.00

10lm

0110

n112

7074

.411

83-6

9.27

154

1.39

8457

16.5

216

.36

2005

.592

70.

877

-0.0

5-0

.174

-0.0

26-0

.078

0.00

70lm

0127

l204

9873

.217

69-7

0.39

849

1.39

8538

16.8

816

.64

2234

.785

60.

887

-0.0

44-0

.162

-0.0

22-0

.072

0.00

10lm

0040

l120

7086

.005

17-6

9.28

234

1.39

9558

16.8

117

.00

1965

.643

50.

948

-0.0

010

-0.0

64-0

.002

0-0

.039

0.00

10lm

0597

l192

7284

.779

25-7

1.78

888

1.40

2455

16.0

315

.75

1259

.609

40.

861

-0.0

41-0

.183

-0.0

18-0

.062

-0.0

010

lm02

00k2

1051

80.5

6212

-67.

7880

81.

4033

6517

.88

17.6

312

37.6

677

0.96

1-0

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-0.0

76-0

.024

-0.0

480.

0080

lm04

57k2

4395

80.2

8756

-66.

0730

31.

4067

117

.81

17.7

215

06.6

956

0.88

7-0

.01

-0.1

60.

0030

-0.0

83-0

.001

0lm

0306

l186

5975

.833

59-6

7.57

889

1.40

7038

17.5

817

.47

1893

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80.

97-0

.038

-0.0

4-0

.009

0-0

.019

0.00

10lm

0166

l126

4173

.179

95-6

8.94

171

1.40

8868

17.5

617

.22

1526

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00.

982

-0.0

63-0

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-0.0

19-0

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-0.0

040

lm03

43n2

5594

84.1

3251

-66.

9085

1.40

9684

15.7

915

.50

1885

.701

50.

88-0

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-0.1

57-0

.01

-0.0

54-0

.002

0lm

0174

l193

7374

.791

43-6

8.64

692

1.41

0559

17.8

717

.73

1971

.642

80.

93-0

.058

-0.1

04-0

.025

-0.0

40.

01lm

0165

n250

5274

.791

52-6

8.64

701

1.41

0581

17.8

817

.68

2208

.581

50.

913

-0.0

6-0

.119

-0.0

34-0

.057

-0.0

010

lm04

33m

7146

77.4

8491

-65.

2367

91.

4136

4616

.31

16.2

022

59.6

061

0.93

1-0

.03

-0.1

01-0

.012

-0.0

49-0

.002

0lm

0440

m22

885

78.2

8887

-65.

0111

31.

4153

7317

.24

17.0

818

05.8

437

0.91

5-0

.032

-0.0

92-0

.008

0-0

.026

0.00

50lm

0332

l249

8980

.934

09-6

6.92

286

1.41

5919

17.5

517

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2160

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40.

957

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030

-0.0

630.

0040

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40.

0080

lm03

32n2

1956

81.4

9459

-66.

8992

81.

4162

6417

.05

16.9

210

86.8

833

0.93

8-0

.047

-0.0

76-0

.012

-0.0

26-0

.002

0lm

0191

l101

6579

.647

41-6

7.85

672

1.41

8043

16.3

016

.04

1433

.810

40.

884

-0.0

31-0

.151

-0.0

13-0

.048

0.00

10lm

0226

k213

7584

.357

7-6

8.86

111.

4180

5517

.47

17.3

718

75.7

102

0.92

40.

0020

-0.1

320.

0010

-0.0

880.

0060

160


0033

m14

746

85.3

1466

-69.

4886

41.

4203

4315

.73

15.6

420

53.5

057

0.94

8-0

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-0.0

58-0

.005

0-0

.011

0.0

lm01

86n6

732

77.4

6315

-68.

9031

51.

4204

3316

.24

16.2

041

8.83

730.

969

-0.0

22-0

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-0.0

050

-0.0

430.

0010

lm01

23n2

3584

73.5

269

-69.

6904

71.

4211

8516

.50

16.2

821

61.7

151

0.98

1-0

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0-0

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-0.0

020

-0.0

15-0

.0lm

0331

k223

1981

.796

09-6

6.39

641.

4214

8516

.26

16.0

917

64.8

726

0.88

1-0

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-0.1

62-0

.018

-0.0

61-0

.001

0lm

0427

k756

975

.483

19-6

5.95

961

1.42

3526

16.5

616

.30

1920

.607

10.

90.

0050

-0.1

530.

0010

-0.0

860.

0010

lm00

90l7

821

78.2

2237

-69.

2583

51.

4254

3317

.63

17.5

014

81.6

316

0.9

-0.0

6-0

.154

-0.0

24-0

.068

0.00

50lm

0454

n540

980

.130

29-6

5.77

294

1.42

6147

16.0

115

.73

760.

8097

0.97

6-0

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0-0

.033

-0.0

020

-0.0

10.

0lm

0021

n514

083

.508

23-6

9.22

983

1.42

9287

16.1

715

.98

1977

.651

70.

967

-0.0

15-0

.03

-0.0

0.00

10-0

.0lm

0467

l111

9682

.140

63-6

6.14

551

1.42

9906

16.3

316

.09

1630

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80.

937

0.0

-0.0

97-0

.001

0-0

.043

-0.0

lm04

75m

1598

484

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21-6

5.64

972

1.43

014

17.3

017

.11

2244

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10.

969

-0.0

2-0

.03

-0.0

030

-0.0

040

0.00

10lm

0225

l185

2385

.443

12-6

8.61

931.

4324

8116

.68

16.5

110

93.8

515

0.89

5-0

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.148

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010

-0.0

650.

0040

lm00

50m

1166

888

.440

83-6

9.12

669

1.43

2856

16.7

416

.47

2211

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00.

981

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040

-0.0

240.

0020

-0.0

13-0

.003

0lm

0030

m97

4484

.469

97-6

9.16

274

1.43

4738

16.3

116

.38

2320

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10.

955

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23-0

.067

-0.0

080

-0.0

41-0

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0lm

0216

m68

0582

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99-6

8.74

527

1.43

6319

16.0

315

.91

1253

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40.

973

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020

-0.0

36-0

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0.0

lm00

80m

5139

94.5

9422

-69.

1927

31.

4364

2717

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17.6

622

94.8

690

0.94

4-0

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15-0

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-0.0

76-0

.002

0lm

0336

n625

581

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3-6

7.48

752

1.43

8008

16.3

216

.03

1904

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30.

923

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3-0

.136

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13-0

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080

lm00

30n5

266

84.2

8567

-69.

2408

61.

4388

4516

.32

16.3

621

83.7

966

0.94

6-0

.01

-0.0

94-0

.003

0-0

.056

-0.0

010

lm03

27m

2371

780

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88-6

7.45

696

1.43

9496

15.9

815

.69

1764

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50.

968

0.00

10-0

.024

-0.0

-0.0

150.

0010

lm01

11m

6204

75.4

8886

-69.

0791

11.

4399

9916

.97

16.7

282

1.81

730.

955

-0.0

22-0

.037

-0.0

010

-0.0

050

0.00

50lm

0030

n192

7584

.423

19-6

9.33

551

1.44

1502

17.7

917

.65

431.

7545

1.00

6-0

.06

-0.0

27-0

.012

-0.0

250.

0040

lm04

83k1

0155

85.3

4155

-65.

2635

1.44

3148

17.7

817

.68

530.

5960

0.90

80.

0-0

.12

-0.0

040

-0.0

45-0

.001

0lm

0365

k199

1787

.056

24-6

7.08

298

1.44

3952

17.6

817

.58

2211

.771

50.

908

-0.0

14-0

.132

0.00

10-0

.089

0.01

lm02

23l2

0472

85.2

7026

-68.

2747

61.

4469

1817

.25

17.1

718

60.6

640

0.95

3-0

.001

0-0

.056

-0.0

020

-0.0

17-0

.0lm

0101

l489

876

.795

01-6

9.23

651.

4477

9717

.36

17.1

815

91.6

497

0.94

8-0

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-0.0

44-0

.025

-0.0

090

-0.0

070

lm01

05l4

144

76.9

2017

-69.

9493

81.

4480

816

.14

15.9

914

68.6

220

0.94

8-0

.03

-0.0

69-0

.007

0-0

.024

0.00

30lm

0424

n177

5874

.858

74-6

5.82

873

1.44

8589

16.5

216

.28

1623

.547

90.

973

-0.0

090

-0.0

39-0

.005

0-0

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-0.0

020

lm03

64k1

1532

86.3

7889

-67.

0327

51.

4489

5816

.88

16.8

022

40.6

680

0.96

-0.0

25-0

.056

-0.0

050

-0.0

160.

0lm

0023

m46

35*

83.6

221

-69.

4251

1.45

0334

17.1

616

.92

1506

.716

30.

924

-0.0

47-0

.11

-0.0

14-0

.046

-0.0

020

lm00

30k1

3920

84.0

5815

-69.

1532

31.

4508

2716

.22

16.1

723

05.7

311

0.94

3-0

.015

-0.0

69-0

.007

0-0

.016

0.00

40lm

0040

k259

7885

.984

18-6

9.22

539

1.45

1215

16.4

116

.32

2202

.803

30.

934

-0.0

13-0

.099

-0.0

070

-0.0

60.

0040

lm01

65m

1831

174

.455

11-6

8.45

461.

4521

2216

.60

16.3

983

5.61

150.

898

-0.0

27-0

.141

-0.0

090

-0.0

440.

0lm

0280

l885

172

.270

03-6

6.45

684

1.45

283

17.6

117

.45

2304

.639

50.

944

0.00

30-0

.083

0.0

-0.0

410.

0030

lm04

40l7

192

77.9

1995

-65.

1138

31.

4530

8717

.63

17.5

711

33.6

887

0.98

-0.0

17-0

.017

0.00

10-0

.00.

0080

lm01

51n1

4381

72.5

678

-67.

8850

31.

4531

2217

.49

17.3

422

26.7

864

0.93

7-0

.01

-0.0

79-0

.005

0-0

.021

-0.0

040

lm00

10m

3763

80.2

6873

-69.

0753

41.

4533

3816

.23

15.5

055

5.54

070.

859

-0.0

31-0

.122

-0.0

1-0

.027

-0.0

030

lm03

37k1

9646

81.9

815

-67.

4385

41.

4539

2117

.55

17.3

970

5.75

390.

972

-0.0

2-0

.052

-0.0

11-0

.037

-0.0

020

lm00

95m

1852

579

.432

39-6

9.85

274

1.45

4941

17.2

717

.39

589.

4691

0.97

6-0

.024

-0.0

36-0

.007

0-0

.013

-0.0

020

lm01

80n1

4087

77.2

7753

-67.

9846

51.

4558

7116

.36

16.1

822

43.6

109

0.91

1-0

.034

-0.1

19-0

.012

-0.0

410.

0lm

0090

k113

3377

.984

84-6

9.12

846

1.45

6551

17.5

217

.61

870.

6308

0.95

50.

0060

-0.0

84-0

.001

0-0

.061

-0.0

030

lm01

56n1

4534

71.8

8183

-68.

9428

61.

4571

17.8

217

.67

2237

.552

60.

978

-0.0

11-0

.047

-0.0

060

-0.0

23-0

.006

0lm

0335

m23

184

82.2

4436

-67.

0914

41.

4577

1516

.60

16.3

444

3.61

440.

982

-0.0

26-0

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-0.0

090

-0.0

180.

0

161

lm06

05n2

3731

87.5

7283

-71.

4432

91.

4581

4917

.02

17.2

115

80.6

986

0.97

6-0

.04

-0.0

25-0

.022

-0.0

080

0.00

60lm

0315

n192

0278

.609

3-6

7.21

954

1.46

0027

15.8

415

.56

800.

6893

0.97

8-0

.014

-0.0

260.

0-0

.00.

0lm

0021

l146

5083

.198

18-6

9.28

828

1.46

2272

15.7

315

.47

1475

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70.

978

-0.0

1-0

.03

-0.0

010

-0.0

050

-0.0

010

lm03

44m

2008

683

.029

73-6

7.08

729

1.46

2707

17.2

417

.08

1576

.696

20.

944

0.00

20-0

.076

-0.0

040

-0.0

510.

0040

lm00

34k9

201

84.1

425

-69.

8144

21.

4639

0216

.55

16.4

013

81.9

065

0.96

8-0

.021

-0.0

37-0

.001

0-0

.005

00.

0020

lm03

35k2

6831

81.7

029

-67.

1175

91.

4647

7417

.45

17.3

438

8.72

340.

964

-0.0

13-0

.057

-0.0

060

-0.0

33-0

.001

0lm

0121

m27

778

73.5

3912

-69.

2162

51.

4651

4617

.26

17.0

448

8.67

620.

963

-0.0

28-0

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-0.0

17-0

.045

-0.0

020

lm01

64k2

6049

72.9

875

-68.

5141

31.

4671

6717

.00

16.7

917

50.8

564

0.94

8-0

.014

-0.0

79-0

.005

0-0

.061

0.00

30lm

0165

n173

7874

.574

54-6

8.60

381

1.46

948

17.2

117

.16

795.

6563

0.96

2-0

.033

-0.0

49-0

.006

0-0

.017

-0.0

lm00

33k9

023

85.0

2569

-69.

4535

31.

4699

7616

.33

16.2

221

74.8

031

0.98

4-0

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24-0

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00.

0010

-0.0

020

lm04

55k3

349

80.4

5913

-65.

5717

91.

4701

6617

.16

17.1

315

29.6

556

0.92

2-0

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-0.0

81-0

.008

0-0

.009

00.

0050

lm00

92n1

6033

78.6

4-6

9.65

524

1.47

342

15.8

215

.61

811.

8528

0.96

20.

0010

-0.0

45-0

.001

0-0

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-0.0

010

lm02

90k1

6764

74.0

6053

-66.

3671

71.

4751

2716

.34

16.1

722

97.6

552

0.98

10.

0030

-0.0

350.

0020

-0.0

230.

0020

lm01

21n2

7034

73.7

4454

-69.

3592

91.

4758

4816

.96

16.7

079

7.65

860.

974

0.00

30-0

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0.00

10-0

.022

-0.0

010

lm02

14k2

5540

82.5

5892

-68.

5152

1.47

6843

17.6

017

.54

2240

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00.

965

-0.0

11-0

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-0.0

040

-0.0

26-0

.004

0lm

0364

n985

586

.495

04-6

7.17

615

1.47

7007

17.6

917

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2223

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00.

947

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060

-0.0

780.

0010

-0.0

54-0

.002

0lm

0294

k139

4473

.964

27-6

7.04

175

1.47

8161

17.0

016

.88

1402

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80.

93-0

.007

0-0

.119

-0.0

040

-0.0

77-0

.0lm

0020

m14

812

82.5

2879

-69.

1460

81.

4787

2516

.14

15.9

119

17.8

257

0.93

7-0

.025

-0.0

75-0

.006

0-0

.02

0.00

50lm

0173

m22

752

76.3

6809

-68.

1256

51.

4792

3216

.81

16.5

518

88.6

122

0.93

7-0

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99-0

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0-0

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0.00

20lm

0173

l292

3375

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28-6

8.31

491.

4801

1516

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16.7

724

96.8

050

0.98

2-0

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0-0

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080

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12-0

.001

0lm

0300

k223

3175

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9-6

6.40

058

1.48

138

17.9

317

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1987

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00.

945

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23-0

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-0.0

15-0

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0.00

50lm

0041

k251

6286

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72-6

9.20

41.

4815

9417

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17.6

019

65.6

435

0.91

40.

0020

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250.

0040

-0.0

6-0

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0347

l578

083

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95-6

7.49

362

1.48

1679

16.0

615

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1495

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10.

966

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070

-0.0

53-0

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0-0

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010

lm03

46k1

2896

82.9

3704

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3948

41.

4817

8416

.90

16.9

555

8.55

930.

975

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1-0

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1-0

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0.00

50lm

0333

m10

861

82.0

787

-66.

6627

1.48

2148

16.0

315

.78

388.

7234

0.98

9-0

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080

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080

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050

0.00

50lm

0556

m65

25*

75.6

8396

-71.

5356

61.

4934

938

16.1

015

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864.

5988

0.96

1-0

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52-0

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2-0

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0lm

0030

n125

00*

84.2

9712

-69.

3905

21.

4997

8415

.82

15.6

611

97.6

811

0.99

5-0

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1-0

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0-0

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0-0

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0346

m23

398

83.0

7818

-67.

4618

31.

5196

8116

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16.2

646

7.60

310.

941

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24-0

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060

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22-0

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0lm

0056

k819

688

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15-7

0.15

366

1.52

3926

16.9

516

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420.

7308

0.94

9-0

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0-0

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0.00

10-0

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0.00

40lm

0350

l571

784

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06-6

6.44

258

1.52

4372

16.1

815

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1835

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20.

954

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21-0

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-0.0

020

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39-0

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0lm

0125

l930

273

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49-6

9.95

682

1.52

6312

16.9

817

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1311

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40.

999

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23-0

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030

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070

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020

lm01

03m

2315

077

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43-6

9.52

645

1.52

7199

17.2

317

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1482

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80.

985

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25-0

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0.00

30-0

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00.

0020

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84l1

1316

76.8

3495

-68.

5777

71.

5299

2217

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17.2

732

7.83

750.

993

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2-0

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090

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16-0

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0lm

0551

k176

7076

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62-7

0.58

525

1.53

2272

17.2

216

.99

1236

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80.

979

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18-0

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020

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020

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23m

9848

73.4

2535

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4539

31.

5341

4517

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17.1

625

16.7

341

0.98

5-0

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030

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110.

0030

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40l1

3585

86.0

081

-69.

2927

61.

5341

6717

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17.4

012

07.7

430

0.96

9-0

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310.

0010

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0.00

20lm

0020

k136

2081

.889

91-6

9.15

231

1.53

4702

16.5

516

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762.

6655

0.91

5-0

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0-0

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1-0

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0.00

20lm

0196

k267

6478

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27-6

8.88

038

1.53

8051

16.6

816

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1901

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50.

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3-0

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13-0

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030

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90l1

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16.2

122

36.7

852

0.98

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90m

4818

78.4

994

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51.

5419

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16.1

813

10.5

084

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00.

0020

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16m

1726

980

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55-7

0.20

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1.54

2338

17.3

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1957

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9474

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0.00

10lm

0573

n131

7380

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14-7

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1.54

5989

17.4

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31-0

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40l8

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919

77.6

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2-0

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0-0

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0.0

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27m

2145

975

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42-6

6.06

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1.54

6547

16.9

716

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2257

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20.

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020

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77-0

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0-0

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0.00

10lm

0026

k106

6581

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62-7

0.17

208

1.54

8267

17.0

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4-0

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14k2

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509

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81n7

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40n7

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90n1

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96-7

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17.5

417

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10.

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38-0

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15-0

.034

-0.0

020

0.00

200.

0030

lm02

85n5

241

73.7

0857

-67.

1363

21.

5577

4515

.93

15.6

419

02.7

300

0.93

7-0

.001

0-0

.076

0.0

-0.0

230.

0010

lm03

41m

1467

083

.817

84-6

6.34

805

1.55

8747

15.9

215

.66

1554

.704

30.

985

-0.0

11-0

.022

-0.0

050

-0.0

11-0

.0lm

0285

m12

790

73.5

3067

-67.

0314

71.

5590

716

.69

16.4

718

19.6

920

0.94

9-0

.013

-0.0

390.

0020

-0.0

040

0.00

80lm

0285

l265

8573

.158

96-6

7.28

642

1.55

9802

17.3

217

.10

815.

8174

0.98

2-0

.012

-0.0

28-0

.004

0-0

.021

-0.0

010

lm03

15m

1016

478

.765

89-6

7.00

723

1.56

0277

16.9

416

.68

1145

.694

50.

975

-0.0

010

-0.0

340.

0010

-0.0

20.

0lm

0110

n256

6874

.282

18-6

9.35

849

1.56

4822

16.3

116

.13

2031

.480

30.

963

-0.0

2-0

.051

-0.0

090

-0.0

28-0

.0lm

0184

l966

076

.885

69-6

8.56

789

1.56

8984

16.2

116

.05

1591

.657

60.

955

0.00

10-0

.066

-0.0

010

-0.0

31-0

.002

0lm

0167

l574

073

.933

2-6

8.89

664

1.57

2604

17.5

617

.36

2183

.662

50.

907

-0.0

-0.1

29-0

.002

0-0

.076

-0.0

050

lm02

14l2

5109

82.3

7873

-68.

6702

1.57

5578

17.4

417

.59

1492

.695

00.

995

-0.0

040

-0.0

29-0

.008

0-0

.017

0.00

10lm

0032

l228

7483

.873

82-6

9.70

626

1.57

6927

15.6

115

.43

1108

.845

70.

867

-0.0

3-0

.147

-0.0

13-0

.057

0.00

20lm

0337

k234

9281

.835

01-6

7.46

624

1.57

8628

17.3

517

.18

1459

.782

20.

963

-0.0

12-0

.07

-0.0

15-0

.041

0.00

40lm

0207

k154

7281

.653

77-6

8.80

021.

5794

2315

.73

15.6

713

17.5

052

0.93

8-0

.024

-0.0

77-0

.011

-0.0

45-0

.002

0lm

0166

l163

9073

.294

55-6

8.96

988

1.57

9747

16.0

915

.81

2245

.778

30.

97-0

.019

-0.0

48-0

.01

-0.0

330.

0030

lm00

23m

7584

83.5

8765

-69.

4420

91.

5798

8716

.13

15.9

022

35.6

280

0.86

4-0

.044

-0.1

85-0

.024

-0.0

860.

0020

lm01

15m

5231

75.3

5313

-69.

7787

21.

5803

7317

.73

17.6

618

62.5

755

0.94

9-0

.002

0-0

.097

-0.0

040

-0.0

640.

0010

lm03

41n6

753

84.0

7502

-66.

4906

41.

5809

6816

.67

16.4

220

14.5

633

0.96

5-0

.011

-0.0

44-0

.003

0-0

.023

0.00

10lm

0593

m12

530

85.2

9938

-70.

8668

11.

5813

9617

.34

17.2

221

99.6

400

0.93

4-0

.055

-0.0

9-0

.027

-0.0

370.

0090

lm01

92n3

0512

79.2

2526

-68.

3380

51.

5835

4716

.95

16.8

422

32.6

252

0.94

6-0

.04

-0.1

25-0

.052

-0.0

790.

01lm

0434

m21

038

76.5

4471

-65.

6932

71.

5855

4716

.29

16.0

614

15.8

778

0.98

8-0

.014

-0.0

29-0

.004

0-0

.015

-0.0

020

lm05

03l1

5319

88.8

0091

-65.

5445

1.58

6779

17.2

717

.19

1931

.733

20.

964

-0.0

7-0

.061

-0.0

44-0

.033

-0.0

010

lm01

72l1

5709

75.0

954

-68.

3373

11.

5880

3417

.55

17.4

620

99.8

753

0.95

0.00

70-0

.096

-0.0

050

-0.0

62-0

.001

0lm

0540

k919

973

.109

41-7

0.50

689

1.58

8396

16.4

016

.15

1813

.731

40.

953

-0.0

16-0

.046

-0.0

020

-0.0

030

0.00

30lm

0335

n574

782

.246

93-6

7.13

654

1.58

8518

17.2

217

.04

1149

.711

30.

947

0.00

80-0

.087

-0.0

060

-0.0

530.

0010

lm01

23m

2270

073

.552

3-6

9.52

692

1.58

8994

16.4

916

.31

556.

5427

0.87

8-0

.048

-0.1

68-0

.019

-0.0

770.

0040

lm01

21n2

5422

73.3

0901

-69.

3815

51.

5906

8117

.37

17.2

318

15.6

981

0.90

2-0

.108

-0.1

6-0

.046

-0.0

92-0

.003

0lm

0376

m12

338

88.5

3671

-67.

3879

61.

5916

1516

.88

16.7

050

3.69

120.

95-0

.015

-0.0

53-0

.004

0-0

.004

00.

0lm

0100

k136

6075

.904

39-6

9.14

193

1.59

1895

16.7

816

.67

1305

.509

40.

944

-0.0

080

-0.0

93-0

.003

0-0

.045

-0.0

030

lm03

87l7

856

90.7

4458

-67.

5176

21.

5922

4316

.65

16.4

419

19.7

987

0.93

5-0

.135

-0.0

97-0

.068

-0.0

430.

0020

163

lm03

30n1

0876

81.2

6355

-66.

4736

71.

5936

1216

.74

16.8

311

50.6

932

0.97

4-0

.015

-0.0

37-0

.006

0-0

.013

-0.0

lm01

20l2

4125

72.0

6416

-69.

3702

81.

5944

817

.42

17.4

111

15.6

637

0.90

80.

0020

-0.1

53-0

.0-0

.088

-0.0

010

lm02

10l2

0271

82.4

3808

-67.

9382

21.

5945

9916

.62

16.4

220

28.5

189

0.88

7-0

.046

-0.1

56-0

.02

-0.0

66-0

.004

0lm

0453

k810

680

.378

16-6

5.24

698

1.59

5613

17.4

817

.34

1840

.725

10.

99-0

.031

-0.0

2-0

.016

-0.0

070

-0.0

040

lm05

50n7

880

75.8

0149

-70.

6544

11.

5968

5817

.14

16.8

622

58.5

811

0.97

9-0

.021

-0.0

29-0

.011

-0.0

170.

0020

lm04

35l5

752

77.2

7269

-65.

7368

31.

5970

3317

.74

17.5

922

24.5

803

0.95

5-0

.072

-0.1

02-0

.036

-0.0

57-0

.003

0lm

0344

m82

9183

.098

27-6

7.01

023

1.59

7243

16.5

416

.36

825.

8571

0.88

3-0

.04

-0.1

59-0

.019

-0.0

710.

0lm

0292

n116

2174

.279

99-6

6.82

953

1.59

9642

16.8

016

.59

1860

.567

20.

973

0.00

30-0

.042

-0.0

020

-0.0

28-0

.006

0lm

0126

k137

5872

.264

26-7

0.20

293

1.60

1905

17.0

316

.85

1918

.601

80.

981

-0.0

22-0

.038

-0.0

1-0

.019

-0.0

040

lm01

54k2

1118

71.3

9661

-68.

4872

1.60

291

17.3

917

.25

1750

.851

10.

964

-0.0

13-0

.052

-0.0

060

-0.0

340.

0030

lm01

75n2

3496

76.5

9228

-68.

6319

1.60

4598

17.4

317

.32

1878

.616

60.

907

-0.0

72-0

.125

-0.0

31-0

.069

-0.0

010

lm01

11m

1609

275

.530

49-6

9.13

855

1.60

4599

16.3

316

.05

1890

.605

60.

94-0

.024

-0.0

67-0

.005

0-0

.019

-0.0

030

lm00

31m

7414

85.6

1249

-69.

0871

31.

6059

8915

.61

15.4

615

91.7

013

0.94

-0.0

18-0

.1-0

.012

-0.0

440.

0010

lm01

75k1

8167

76.0

6658

-68.

4525

61.

6062

0616

.47

16.3

314

02.8

984

0.93

8-0

.023

-0.0

76-0

.005

0-0

.016

0.0

lm00

44l2

3659

85.8

3336

-70.

0552

1.60

7072

16.3

916

.20

1481

.736

30.

876

-0.0

75-0

.169

-0.0

26-0

.082

0.00

10lm

0197

k234

6779

.842

63-6

8.84

883

1.60

8347

16.3

216

.07

1918

.710

40.

975

-0.0

11-0

.028

-0.0

070

-0.0

110.

0020

lm03

25n2

3385

80.4

343

-67.

2488

31.

6090

117

.10

16.8

820

58.4

899

0.95

3-0

.0-0

.057

-0.0

020

-0.0

250.

0010

lm00

52m

1892

688

.608

4-6

9.55

504

1.61

1031

16.0

515

.77

1566

.720

30.

964

-0.0

25-0

.056

-0.0

070

-0.0

260.

0010

lm01

61n2

4107

74.5

1188

-67.

9418

21.

6114

7517

.76

17.5

615

64.5

855

0.97

8-0

.03

-0.0

250.

0020

-0.0

030

0.00

70lm

0367

n683

587

.455

23-6

7.50

409

1.61

154

17.7

317

.52

2033

.544

70.

971

-0.0

030

-0.0

68-0

.001

0-0

.061

-0.0

040

lm02

15m

2258

583

.794

33-6

8.48

498

1.61

3457

17.4

517

.22

2155

.804

70.

969

-0.0

2-0

.059

-0.0

13-0

.046

-0.0

010

lm06

03l2

4970

86.8

177

-71.

0998

61.

6142

2717

.27

17.2

410

87.8

655

0.88

7-0

.079

-0.1

95-0

.042

-0.1

020.

0030

lm00

30k1

3205

83.9

8549

-69.

1476

41.

6152

0516

.09

16.1

118

08.8

535

0.90

6-0

.03

-0.1

13-0

.011

-0.0

370.

0030

lm05

50m

2019

675

.552

69-7

0.58

644

1.61

6823

17.3

117

.09

1126

.615

20.

979

-0.0

18-0

.05

-0.0

080

-0.0

35-0

.0lm

0294

k319

574

.152

99-6

6.97

358

1.62

0032

17.1

817

.08

1173

.624

40.

981

-0.0

16-0

.033

-0.0

070

-0.0

2-0

.002

0lm

0156

m42

6271

.910

81-6

8.85

731.

6202

6415

.97

15.7

822

57.5

616

0.93

3-0

.019

-0.0

78-0

.004

0-0

.021

-0.0

lm04

25n1

5511

75.6

5717

-65.

8027

31.

6233

8417

.71

17.5

116

03.5

934

0.97

2-0

.016

-0.0

50.

0080

-0.0

41-0

.007

0lm

0426

l157

0274

.426

31-6

6.16

279

1.62

4957

15.7

215

.46

508.

6286

0.89

7-0

.03

-0.1

1-0

.01

-0.0

310.

0070

lm02

10l1

8828

82.5

2517

-67.

9267

11.

6258

9717

.63

17.5

423

02.7

223

0.91

-0.0

47-0

.074

-0.0

16-0

.025

0.00

80lm

0710

k102

8582

.931

66-7

1.92

374

1.62

7842

17.7

117

.66

1593

.682

30.

969

-0.0

050

-0.0

450.

0010

-0.0

30.

0010

lm00

90n2

9958

78.5

351

-69.

3833

11.

6284

0717

.44

17.3

521

64.7

591

0.93

8-0

.009

0-0

.097

-0.0

070

-0.0

57-0

.002

0lm

0344

k106

0182

.550

39-6

7.02

696

1.62

8604

16.6

616

.51

1441

.789

00.

912

-0.0

34-0

.107

-0.0

15-0

.039

0.00

20lm

0711

m42

1884

.538

37-7

1.86

447

1.63

0559

17.3

417

.24

488.

7207

0.89

1-0

.035

-0.0

94-0

.007

0-0

.012

0.02

6lm

0236

l256

4086

.268

2-6

9.03

441.

6313

1217

.32

17.1

094

1.54

170.

842

-0.0

5-0

.202

-0.0

050

-0.0

840.

015

lm05

84l6

042

81.6

7559

-71.

3408

71.

6323

4417

.07

17.1

019

57.6

888

0.93

9-0

.039

-0.0

78-0

.01

-0.0

3-0

.001

0lm

0151

m41

2872

.466

64-6

7.70

253

1.63

3059

15.9

515

.58

1465

.656

40.

906

0.00

40-0

.155

0.00

30-0

.093

0.00

30lm

0424

n101

3374

.977

82-6

5.77

246

1.63

539

16.3

016

.08

706.

7728

0.98

5-0

.016

-0.0

29-0

.006

0-0

.016

0.0

lm00

93n2

4281

79.2

7628

-69.

6823

91.

6357

9917

.49

17.3

555

6.51

910.

925

-0.0

070

-0.1

41-0

.0-0

.078

-0.0

020

lm02

04m

1867

981

.155

2-6

8.45

898

1.63

6472

17.4

417

.36

1455

.769

20.

963

-0.0

19-0

.04

-0.0

080

-0.0

270.

0010

lm02

01n2

6407

82.1

4915

-67.

9539

11.

6386

717

.71

17.4

710

93.8

296

0.94

1-0

.015

-0.0

5-0

.009

0-0

.021

0.00

10lm

0333

k991

581

.696

75-6

6.65

927

1.63

9068

16.5

816

.40

2245

.677

30.

955

-0.0

090

-0.0

59-0

.005

0-0

.025

-0.0

020

164


0090

m43

2178

.601

31-6

9.07

897

1.64

1272

17.1

917

.04

1231

.610

10.

906

-0.0

57-0

.118

-0.0

25-0

.052

0.00

40lm

0032

m22

261

84.3

5161

-69.

5720

31.

6441

4615

.70

15.4

823

45.5

978

0.97

4-0

.007

0-0

.038

-0.0

090

-0.0

3-0

.003

0lm

0551

l210

8175

.922

28-7

0.73

455

1.64

5211

15.6

815

.48

1903

.745

30.

963

-0.0

16-0

.037

0.0

-0.0

010

-0.0

010

lm03

54m

1387

584

.965

51-6

7.04

351

1.64

5882

17.3

617

.22

819.

8363

0.98

3-0

.012

-0.0

230.

0030

-0.0

020

-0.0

050

lm03

14k2

4373

77.6

4572

-67.

1111

81.

6491

7916

.35

16.3

021

86.7

216

0.87

9-0

.057

-0.1

66-0

.028

-0.0

750.

0020

lm00

52l4

698

88.1

0094

-69.

5857

91.

6509

7917

.20

17.0

515

49.7

634

0.93

6-0

.01

-0.0

99-0

.009

0-0

.058

0.00

40lm

0551

l153

6576

.072

1-7

0.69

851.

6520

8316

.25

15.9

812

66.5

146

0.98

8-0

.008

0-0

.028

-0.0

050

-0.0

21-0

.001

0lm

0101

l229

0076

.920

21-6

9.34

193

1.65

3449

16.2

616

.14

1139

.845

20.

891

-0.0

26-0

.122

-0.0

1-0

.032

0.00

30lm

0310

m15

759

77.9

497

-66.

4224

61.

6536

5817

.30

17.1

012

57.5

597

0.98

2-0

.024

-0.0

19-0

.001

00.

0010

-0.0

040

lm03

15n1

4721

78.6

2626

-67.

1917

51.

6549

9716

.87

16.5

717

86.7

429

0.97

7-0

.002

0-0

.037

0.00

10-0

.02

0.00

30lm

0317

k486

978

.577

66-6

7.33

758

1.65

617

17.7

117

.50

776.

7495

0.98

4-0

.006

0-0

.059

-0.0

090

-0.0

54-0

.006

0lm

0304

n255

3576

.067

79-6

7.26

431.

6572

4515

.76

15.4

622

48.7

779

0.99

9-0

.002

0-0

.017

-0.0

060

-0.0

110.

0010

lm00

33k1

5395

85.0

6121

-69.

4932

61.

6580

115

.92

15.8

522

57.6

709

0.90

8-0

.04

-0.1

16-0

.013

-0.0

440.

0020

lm00

30l4

662

84.0

9164

-69.

2367

91.

6606

5116

.99

17.1

714

68.6

786

0.92

80.

0040

-0.1

2-0

.001

0-0

.078

0.00

40lm

0344

l240

7682

.641

83-6

7.27

292

1.66

2852

16.3

016

.12

1447

.834

90.

933

-0.0

22-0

.077

-0.0

020

-0.0

11-0

.0lm

0325

k980

580

.318

71-6

7.01

041.

6643

5116

.19

15.9

511

66.6

467

0.94

9-0

.007

0-0

.073

-0.0

010

-0.0

390.

0030

lm02

07n1

8537

82.0

2376

-68.

9846

71.

6647

7715

.60

15.3

623

18.6

740

0.95

9-0

.018

-0.0

510.

0-0

.009

00.

0040

lm05

83l2

2712

82.3

5358

-71.

0823

61.

6655

6515

.60

15.4

412

53.6

088

0.94

8-0

.015

-0.0

87-0

.008

0-0

.048

-0.0

010

lm03

51m

1277

385

.822

24-6

6.32

968

1.66

6009

16.4

216

.15

1865

.694

30.

976

-0.0

54-0

.049

-0.0

19-0

.041

-0.0

010

lm03

64m

5107

86.6

1851

-66.

9854

51.

6662

3117

.45

17.2

814

39.8

010

0.92

9-0

.001

0-0

.132

0.00

10-0

.082

0.00

10lm

0377

n700

089

.184

35-6

7.51

179

1.66

7075

17.2

116

.93

1625

.666

70.

952

-0.0

12-0

.066

-0.0

090

-0.0

260.

0020

lm02

12n2

0573

83.0

2989

-68.

2850

41.

6680

9216

.91

16.9

419

53.7

398

0.92

9-0

.011

-0.1

15-0

.008

0-0

.085

0.0

lm03

47l1

7494

83.7

5017

-67.

5900

31.

6689

0116

.46

16.3

110

93.8

434

0.98

3-0

.012

-0.0

26-0

.006

0-0

.01

0.00

10lm

0216

l879

382

.576

22-6

8.92

088

1.66

9043

15.8

615

.68

1997

.580

30.

928

-0.0

31-0

.103

-0.0

020

-0.0

34-0

.006

0lm

0127

n645

573

.559

84-7

0.29

475

1.66

9262

16.3

216

.07

1958

.599

60.

887

-0.0

5-0

.161

-0.0

22-0

.062

-0.0

010

lm01

74k2

3286

74.9

3274

-68.

4936

81.

6697

8217

.56

17.4

722

06.7

780

0.94

9-0

.034

-0.0

65-0

.014

-0.0

190.

0050

lm01

55k1

7320

72.1

6521

-68.

4585

11.

6707

8617

.40

17.3

719

80.5

256

0.96

8-0

.083

-0.0

6-0

.028

-0.0

5-0

.002

0lm

0460

l231

1881

.202

9-6

5.17

684

1.67

0908

17.6

717

.59

1424

.890

10.

924

-0.0

15-0

.13

-0.0

050

-0.0

68-0

.004

0lm

0473

l153

0983

.709

99-6

5.44

981

1.67

1121

17.3

917

.32

1885

.706

30.

962

-0.0

7-0

.059

-0.0

47-0

.035

0.00

20lm

0184

k228

0776

.852

44-6

8.49

225

1.67

2505

16.8

516

.66

1583

.660

10.

964

-0.0

27-0

.082

-0.0

15-0

.062

-0.0

010

lm00

30m

3468

84.4

2029

-69.

0781

21.

6740

9816

.18

16.1

122

64.7

604

0.92

7-0

.01

-0.1

18-0

.009

0-0

.08

0.00

40lm

0127

m85

8973

.762

25-7

0.15

474

1.67

6613

17.1

416

.98

2297

.631

80.

959

-0.0

22-0

.032

0.0

0.00

200.

0050

lm00

35m

2323

385

.696

45-6

9.88

486

1.67

7625

15.5

815

.34

797.

5962

0.95

1-0

.014

-0.0

420.

00.

00.

0lm

0156

m16

1971

.732

44-6

8.76

539

1.68

1305

17.1

517

.03

1864

.561

30.

993

0.00

20-0

.02

-0.0

-0.0

15-0

.002

0lm

0113

k252

5974

.862

16-6

9.53

946

1.68

1418

17.4

517

.39

858.

7184

0.97

7-0

.019

-0.0

32-0

.001

00.

0010

0.00

30lm

0356

l710

084

.697

1-6

7.50

193

1.68

2072

16.9

616

.81

2185

.704

00.

923

-0.0

29-0

.08

-0.0

12-0

.026

0.0

lm03

44l1

3598

82.6

2982

-67.

2010

51.

6853

9516

.39

16.1

545

0.81

850.

919

0.00

10-0

.129

-0.0

020

-0.0

89-0

.001

0lm

0376

n112

3088

.291

72-6

7.53

606

1.68

6368

17.5

917

.41

1664

.548

60.

965

-0.0

060

-0.1

15-0

.017

-0.0

760.

0090

lm01

06l1

6000

76.1

9455

-70.

3658

1.68

6602

17.4

517

.29

1779

.778

80.

936

0.00

40-0

.088

-0.0

050

-0.0

52-0

.001

0lm

0377

l92

89.0

9938

-67.

6003

61.

6876

7717

.60

17.3

776

1.75

830.

956

-0.0

45-0

.074

-0.0

22-0

.041

-0.0

040

lm00

55l7

331

88.7

6966

-69.

9460

81.

6884

7917

.40

17.3

919

11.8

249

0.97

7-0

.004

0-0

.02

-0.0

020

-0.0

19-0

.003

0

165

lm04

24n1

7990

74.7

9369

-65.

8914

1.69

0344

17.0

216

.79

2198

.633

60.

96-0

.018

-0.0

78-0

.01

-0.0

590.

0030

lm03

40n5

950

83.0

4071

-66.

4409

91.

6925

7715

.68

15.4

716

07.6

250

0.91

6-0

.001

0-0

.143

0.0

-0.0

890.

0040

lm00

21m

1520

783

.333

7-6

9.13

687

1.69

5205

17.5

017

.39

1145

.703

00.

874

-0.0

75-0

.177

-0.0

41-0

.099

0.01

4lm

0186

m18

764

77.3

7196

-68.

8263

31.

6970

3115

.73

15.5

522

57.6

156

0.96

50.

0030

-0.0

50.

0030

-0.0

32-0

.002

0lm

0344

k440

982

.525

54-6

6.98

509

1.69

7053

16.2

816

.09

1616

.587

10.

950.

0010

-0.0

89-0

.0-0

.053

-0.0

010

lm01

21l1

5224

72.8

0434

-69.

2925

41.

6997

0816

.64

16.5

110

90.6

622

0.97

4-0

.023

-0.0

36-0

.001

0-0

.013

0.00

10lm

0221

n123

9885

.799

38-6

7.87

471

1.70

0592

17.3

917

.20

1889

.696

90.

908

-0.0

030

-0.1

230.

0010

-0.0

590.

0020

lm01

60m

2404

573

.420

43-6

7.80

215

1.70

2329

16.2

516

.01

1898

.736

90.

88-0

.028

-0.1

34-0

.011

-0.0

230.

0010

lm02

15k2

5234

83.5

4176

-68.

5006

51.

7027

1116

.67

16.5

713

75.8

974

0.95

6-0

.031

-0.0

61-0

.005

0-0

.021

-0.0

030

lm02

14n4

693

82.9

0646

-68.

5338

91.

7027

5417

.44

17.5

221

78.7

367

0.97

50.

0010

-0.0

66-0

.002

0-0

.049

-0.0

090

lm06

04k1

9867

85.5

5982

-71.

2818

61.

7028

3616

.50

16.5

044

5.72

790.

962

-0.0

12-0

.069

-0.0

11-0

.048

-0.0

030

lm03

15k1

9071

78.2

3229

-67.

0672

91.

7029

5317

.17

17.0

640

1.75

880.

988

-0.0

1-0

.019

-0.0

030

-0.0

10.

0020

lm00

85k5

094

94.9

5248

-69.

7825

1.70

5211

16.4

816

.33

2223

.689

90.

98-0

.016

-0.0

20.

0010

0.0

0.00

10lm

0167

n606

474

.666

38-6

8.89

41.

7081

216

.65

16.4

418

88.5

883

0.98

6-0

.011

-0.0

33-0

.006

0-0

.023

-0.0

020

lm01

60k1

5778

73.3

0671

-67.

7540

11.

7092

1116

.65

16.3

718

11.7

418

0.88

8-0

.039

-0.1

55-0

.019

-0.0

530.

0010

lm01

55k2

2815

72.3

7866

-68.

4916

21.

7101

2816

.93

17.0

019

07.7

234

0.97

2-0

.061

-0.0

42-0

.015

-0.0

27-0

.003

0lm

0131

l128

4671

.289

77-6

9.39

025

1.71

0566

16.2

316

.09

870.

5622

0.96

6-0

.024

-0.0

51-0

.008

0-0

.021

0.00

40lm

0587

k277

4282

.469

04-7

1.67

718

1.71

1556

16.4

316

.19

1208

.747

30.

975

-0.0

15-0

.025

0.0

-0.0

020

0.0

lm01

11m

7486

75.3

29-6

9.08

815

1.71

3146

17.4

017

.16

2171

.700

40.

932

0.0

-0.1

1-0

.002

0-0

.063

0.00

30lm

0207

m26

339

81.8

4312

-68.

8687

91.

7150

1516

.11

15.8

918

03.8

386

0.84

7-0

.051

-0.1

67-0

.027

-0.0

790.

0040

lm04

47n7

830

79.2

0754

-66.

1082

21.

7155

6117

.47

17.2

722

25.6

609

0.89

2-0

.063

-0.1

34-0

.024

-0.0

60.

0040

lm03

26k2

3448

79.1

6561

-67.

4577

31.

7160

3616

.92

16.8

120

28.5

100

0.94

2-0

.014

-0.0

98-0

.008

0-0

.054

0.00

30lm

0292

n164

8374

.369

28-6

6.86

049

1.71

682

15.6

715

.42

2471

.886

80.

972

-0.0

11-0

.03

-0.0

020

0.00

10-0

.002

0lm

0050

n202

8088

.647

21-6

9.38

678

1.71

811

17.5

717

.45

871.

6393

0.96

20.

0010

-0.0

590.

0010

-0.0

360.

0010

lm03

44n5

050

83.0

0607

-67.

1404

51.

7189

516

.62

16.4

513

64.9

387

0.98

1-0

.02

-0.0

22-0

.006

0-0

.011

0.00

50lm

0347

k177

2283

.538

96-6

7.42

469

1.72

4282

16.8

916

.78

1768

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00.

957

0.00

70-0

.072

-0.0

010

-0.0

540.

0020

lm03

20n1

9241

79.7

2365

-66.

5277

51.

7247

7417

.04

16.9

112

58.5

611

0.99

3-0

.036

-0.0

080

-0.0

090

-0.0

070

-0.0

020

lm01

17k2

6536

75.0

7509

-70.

2802

51.

7257

8816

.89

16.6

379

7.59

990.

972

-0.0

15-0

.047

-0.0

070

-0.0

27-0

.003

0lm

0366

m35

4386

.482

29-6

7.32

311

1.72

7942

17.0

816

.97

1828

.802

80.

895

-0.0

56-0

.137

-0.0

22-0

.054

0.00

30lm

0285

l175

4373

.299

65-6

7.21

674

1.72

8627

16.2

515

.98

1838

.676

10.

977

-0.0

13-0

.036

-0.0

030

-0.0

090

-0.0

010

lm01

26l2

0410

72.0

8139

-70.

3952

61.

7291

8516

.94

16.9

018

60.5

466

0.93

9-0

.05

-0.1

11-0

.026

-0.0

64-0

.002

0lm

0333

k279

2581

.906

91-6

6.76

681

1.73

1749

17.5

517

.49

1883

.664

50.

893

-0.0

66-0

.144

-0.0

3-0

.07

-0.0

040

lm01

10k2

3246

74.0

4754

-69.

1985

31.

7320

1815

.94

15.7

417

55.8

812

0.89

9-0

.032

-0.1

27-0

.013

-0.0

43-0

.001

0lm

0354

n956

484

.742

62-6

7.17

105

1.73

5055

16.9

416

.80

1305

.563

20.

982

-0.0

16-0

.02

0.0

0.0

-0.0

lm01

25k2

2446

72.9

9053

-69.

8850

81.

7351

8616

.64

16.5

616

00.5

591

0.90

6-0

.038

-0.1

26-0

.017

-0.0

550.

0040

lm01

14m

1515

174

.594

23-6

9.83

697

1.74

1331

17.2

017

.09

1605

.544

50.

945

-0.0

12-0

.1-0

.009

0-0

.081

-0.0

020

lm06

23m

1743

191

.496

37-7

0.91

431

1.74

138

17.5

917

.43

2307

.773

80.

976

-0.0

52-0

.052

-0.0

1-0

.029

-0.0

010

lm03

45k3

891

83.7

1194

-66.

9797

21.

7424

8615

.98

15.7

950

7.57

860.

881

-0.0

57-0

.17

-0.0

27-0

.08

0.00

30lm

0317

k171

6278

.188

83-6

7.42

939

1.74

4914

16.3

516

.18

1529

.629

50.

953

-0.0

070

-0.0

73-0

.004

0-0

.043

-0.0

020

lm07

00k1

3942

80.5

0345

-71.

9429

31.

7463

6117

.33

17.1

211

90.7

323

0.97

9-0

.028

-0.0

29-0

.001

0-0

.001

00.

0060

lm07

10k7

222

82.6

1599

-71.

9023

21.

7464

7617

.28

17.0

718

89.8

399

0.96

6-0

.024

-0.0

34-0

.001

00.

0020

0.00

30

166


0127

l673

173

.212

6-7

0.29

473

1.74

8158

15.4

915

.21

1992

.517

80.

896

-0.0

41-0

.133

-0.0

15-0

.045

-0.0

020

lm01

27m

9330

73.6

3977

-70.

1607

41.

7511

6115

.87

15.6

725

55.6

741

0.98

7-0

.011

-0.0

140.

0010

-0.0

010

0.00

30lm

0181

m21

196

78.0

2705

-67.

7727

21.

7514

9116

.77

16.7

412

71.5

380

0.99

-0.0

43-0

.012

-0.0

090

-0.0

110.

0010

lm02

05n1

5591

81.8

3723

-68.

5895

41.

7536

9716

.30

16.0

037

7.81

220.

98-0

.012

-0.0

3-0

.005

0-0

.016

0.00

30lm

0356

k552

684

.674

36-6

7.33

731

1.75

4305

17.5

117

.53

1842

.860

30.

925

-0.0

020

-0.0

98-0

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-0.0

610.

0040

lm05

64l6

100

77.3

2867

-71.

3353

51.

7544

8816

.79

16.5

418

44.7

313

0.97

10.

0040

-0.0

650.

0010

-0.0

45-0

.001

0lm

0285

n732

273

.694

27-6

7.15

244

1.75

4575

16.4

716

.16

1091

.663

80.

963

-0.0

030

-0.0

41-0

.003

0-0

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0.00

30lm

0112

n127

7574

.607

44-6

9.62

906

1.75

6539

15.8

315

.66

2231

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70.

987

-0.0

010

-0.0

26-0

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0-0

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0.0

lm04

36l1

4585

76.4

2263

-66.

1591

71.

7569

7116

.04

15.6

518

64.6

055

0.96

4-0

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-0.0

57-0

.012

-0.0

34-0

.002

0lm

0184

n982

477

.501

89-6

8.56

479

1.75

7143

16.1

415

.97

2084

.911

90.

965

0.00

10-0

.057

0.00

20-0

.038

-0.0

010

lm00

20m

1062

182

.486

96-6

9.12

021.

7588

7615

.39

15.2

518

75.6

794

0.98

60.

0010

-0.0

26-0

.001

0-0

.01

0.00

10lm

0223

m18

449

85.7

7103

-68.

1128

1.75

9816

16.8

716

.66

1101

.878

40.

94-0

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52-0

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0-0

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00.

0lm

0090

l212

3677

.964

17-6

9.34

711

1.76

0117

.35

17.2

653

0.55

690.

964

-0.0

12-0

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-0.0

080

-0.0

46-0

.002

0lm

0030

n222

7884

.361

-69.

3554

1.76

0563

16.7

816

.69

2226

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70.

956

-0.0

-0.0

52-0

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0-0

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0.0

lm00

95l3

0693

78.9

2326

-70.

0776

21.

7610

1616

.00

15.8

215

79.7

005

0.89

5-0

.001

0-0

.14

0.00

10-0

.066

0.00

20lm

0217

n248

8584

.039

69-6

8.92

426

1.76

2408

16.2

716

.18

802.

8084

0.93

70.

0-0

.108

-0.0

020

-0.0

750.

0050

lm03

43m

9142

83.8

3843

-66.

6530

41.

7635

5616

.69

16.5

846

8.65

780.

917

-0.0

53-0

.109

-0.0

2-0

.05

0.00

40lm

0045

n247

5487

.405

13-7

0.09

581

1.76

449

16.8

116

.51

819.

7090

0.98

3-0

.011

-0.0

28-0

.004

0-0

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0.00

40lm

0206

k180

0480

.536

53-6

8.81

668

1.76

5559

16.8

216

.71

1595

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80.

894

-0.0

59-0

.156

-0.0

22-0

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-0.0

050

lm04

46k1

2751

77.9

4-6

5.99

113

1.76

6655

17.1

016

.95

1904

.749

90.

965

-0.0

2-0

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-0.0

1-0

.05

0.00

40lm

0304

n290

8475

.991

17-6

7.28

674

1.77

2755

15.8

015

.52

1628

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00.

981

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12-0

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060

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080

0.0

lm02

23n1

9445

85.6

5399

-68.

342

1.77

3336

17.3

017

.17

1122

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60.

983

-0.0

21-0

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0.00

100.

0010

0.00

10lm

0283

k137

5573

.164

4-6

6.69

281.

7744

0916

.51

16.3

441

4.73

840.

965

-0.0

19-0

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0.0

0.0

0.00

10lm

0550

k195

7775

.292

69-7

0.58

692

1.77

4651

16.0

415

.74

2304

.684

80.

99-0

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0-0

.03

0.0

-0.0

23-0

.001

0lm

0291

m21

869

75.0

7896

-66.

3838

1.77

4816

17.4

017

.17

1820

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20.

931

-0.0

9-0

.112

-0.0

39-0

.062

0.00

10lm

0101

k866

977

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02-6

9.10

507

1.77

5599

16.4

916

.23

1305

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40.

987

-0.0

18-0

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020

-0.0

030

-0.0

050

lm01

07k1

8605

77.0

512

-70.

2212

11.

7766

4416

.94

16.7

322

59.6

017

0.95

3-0

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-0.0

62-0

.006

0-0

.029

-0.0

020

lm02

41m

1803

489

.226

76-6

7.77

295

1.77

7518

17.4

417

.25

1255

.648

60.

972

-0.0

1-0

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-0.0

050

-0.0

180.

0010

lm03

47m

2208

083

.968

17-6

7.45

279

1.77

7695

15.6

615

.38

428.

7524

0.96

1-0

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-0.0

57-0

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0-0

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-0.0

010

lm00

12l1

6381

79.9

1597

-69.

6584

21.

7790

215

.96

15.6

837

6.87

290.

949

-0.0

28-0

.08

-0.0

090

-0.0

15-0

.002

0lm

0031

m22

434

85.6

1171

-69.

1946

61.

7790

4917

.32

17.2

111

81.7

833

0.97

8-0

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-0.0

61-0

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0-0

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030

lm05

43k1

2503

74.1

7109

-70.

8689

31.

7804

6817

.12

16.9

915

67.6

014

0.97

2-0

.01

-0.0

31-0

.003

0-0

.007

0-0

.002

0lm

0110

n110

1574

.565

63-6

9.26

961.

7817

0416

.04

15.8

211

39.8

417

0.97

8-0

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-0.0

16-0

.001

00.

00.

0010

lm02

17l1

7550

83.3

8491

-68.

9815

91.

7842

0116

.77

16.7

025

56.7

273

0.97

3-0

.01

-0.0

28-0

.005

0-0

.017

-0.0

lm00

14m

1494

0*80

.454

21-6

9.83

811.

7856

3417

.27

17.1

517

11.9

362

0.97

6-0

.008

0-0

.044

-0.0

040

-0.0

18-0

.003

0lm

0120

m68

4072

.476

89-6

9.08

672

1.78

5889

17.1

316

.96

1777

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40.

958

-0.0

26-0

.041

-0.0

010

-0.0

020

0.00

40lm

0313

k199

3978

.399

02-6

6.71

775

1.78

7155

17.2

617

.17

1097

.654

70.

879

-0.0

67-0

.163

-0.0

31-0

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0.00

40lm

0031

m11

024

85.6

2526

-69.

2203

11.

7887

4117

.59

17.5

422

30.6

328

0.92

5-0

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0-0

.12

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030

-0.0

62-0

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0lm

0167

m10

826

74.4

7513

-68.

7739

11.

7887

7916

.05

15.8

511

81.6

320

0.98

6-0

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15-0

.001

0-0

.001

0-0

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0290

l521

373

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04-6

6.43

437

1.79

1025

15.4

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.28

2201

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70.

932

-0.0

28-0

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-0.0

11-0

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lm02

85n1

2253

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.377

58-6

7.19

251.

7919

9817

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16.9

315

24.5

967

0.92

3-0

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0-0

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080

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050.

0020

167

lm03

44l1

6103

82.6

3064

-67.

2183

11.

7929

415

.60

15.3

615

76.6

962

0.98

3-0

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0-0

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-0.0

050

-0.0

30.

0010

lm01

22m

1943

672

.568

34-6

9.55

117

1.79

6151

16.2

516

.15

1825

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10.

945

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010

-0.0

69-0

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0-0

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-0.0

lm01

21k7

851

73.2

5922

-69.

0930

51.

7976

3716

.56

16.2

922

65.5

959

0.96

1-0

.01

-0.0

88-0

.003

0-0

.052

0.00

20lm

0284

n225

8372

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71-6

7.26

464

1.79

8432

16.9

016

.71

1579

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70.

958

-0.0

2-0

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-0.0

-0.0

060

0.00

10lm

0053

k119

4189

.148

92-6

9.47

271

1.79

9736

17.5

517

.53

800.

7358

0.91

3-0

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24-0

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620.

0040

lm03

00k5

450

75.8

4331

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2824

51.

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4716

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15.7

541

9.59

640.

969

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14-0

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0.00

10-0

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0050

lm01

64m

2801

073

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27-6

8.51

651.

8017

6217

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17.2

373

3.70

680.

978

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1-0

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0.00

20-0

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0.0

lm04

67k1

1376

82.0

8206

-65.

9833

71.

8021

7515

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15.3

422

15.8

423

0.92

5-0

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09-0

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-0.0

43-0

.001

0lm

0497

m32

9487

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41-6

5.98

825

1.80

2402

17.0

116

.77

1828

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30.

944

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34-0

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070

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2-0

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0lm

0173

m15

001

76.3

9634

-68.

081.

8030

3517

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17.3

018

80.5

939

0.97

3-0

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31-0

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260.

0010

lm00

10l2

4269

80.1

0633

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3668

31.

8038

3815

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15.7

411

97.6

493

0.99

2-0

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0-0

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020

lm04

55n9

465

80.8

8538

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7585

81.

8047

2617

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17.0

214

47.8

054

0.96

1-0

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65-0

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-0.0

53-0

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0lm

0336

l200

1181

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75-6

7.63

918

1.80

7377

17.1

516

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533.

5488

0.94

0.00

10-0

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020

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630.

0lm

0342

k470

882

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24-6

6.63

464

1.80

7389

16.9

716

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1952

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00.

952

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48-0

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-0.0

14-0

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0.00

30lm

0340

l195

9482

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36-6

6.58

521

1.80

9525

15.5

815

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1388

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20.

875

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55-0

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26-0

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0.00

10lm

0551

l860

876

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12-7

0.65

461.

8097

8316

.84

16.5

711

83.6

547

0.98

5-0

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060.

0030

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81-0

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lm01

12n1

2177

74.3

9924

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6260

71.

8126

6515

.44

15.2

722

56.5

889

0.96

2-0

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39-0

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00.

0030

lm03

34l2

0839

80.9

4674

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2968

61.

8132

5516

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15.7

710

59.8

849

0.95

8-0

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47-0

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0-0

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0-0

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0lm

0323

m29

284

80.3

3912

-66.

7768

51.

8148

7917

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17.4

217

01.4

666

0.95

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42-0

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0050

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46k1

7569

86.1

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2370

51.

8152

1616

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16.7

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39.6

243

0.90

8-0

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07-0

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440.

0090

lm02

57m

2028

1*91

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33-6

8.85

292

1.82

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17.3

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70.

951

0.00

30-0

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0.00

20-0

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0.00

10lm

0555

m84

1576

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04-7

1.20

828

1.82

1561

16.4

716

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1093

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10.

978

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27-0

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0-0

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0.0

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83l1

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82.4

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11.

8223

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15.8

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06.5

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0.96

9-0

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58-0

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350.

0010

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53l1

6176

85.3

1671

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8604

81.

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5717

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17.1

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60.7

184

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520.

0060

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35l1

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71.0

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61.

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8317

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16.9

222

34.5

602

0.89

7-0

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53-0

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-0.0

61-0

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0lm

0340

m67

9283

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16-6

6.29

128

1.82

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16.5

216

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2240

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80.

981

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45k1

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86.9

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6116

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16.1

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1.81

330.

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23-0

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86n1

1896

77.3

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71.

8279

917

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16.9

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30.7

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0.94

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0-0

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3lm

0131

n108

39*

71.6

3107

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2634

71.

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17.5

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20.6

538

0.91

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0.01

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15l2

3100

73.7

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8615

61.

8304

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16.2

415

99.5

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0.96

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090

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470.

0090

lm01

66m

1307

773

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42-6

8.78

261

1.83

2137

16.9

617

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838.

6081

0.89

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30-0

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0231

l245

0187

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48-6

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1.83

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16.6

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6922

0.97

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140.

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0.00

400.

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0305

l177

9676

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45-6

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93n1

3361

80.3

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81.

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17.4

118

62.6

168

0.97

5-0

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6-0

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0-0

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020

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21m

2486

573

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49-6

9.19

693

1.83

5103

16.0

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1640

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31-0

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15-0

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050

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94k2

4995

73.9

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1107

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5415

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15.8

131

7.85

960.

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21k2

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75.6

187

0.96

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0020

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14k1

7880

74.0

8566

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8622

81.

8420

7517

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16.8

521

92.6

912

0.97

4-0

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31-0

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0-0

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0.00

10lm

0033

k287

284

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54-6

9.41

477

1.84

2642

17.2

317

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1838

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10.

945

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11-0

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050

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90.

0010

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13k2

5910

83.4

9101

-68.

1480

41.

8437

7817

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17.2

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85.6

921

0.96

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0211

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88-6

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8447

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16.4

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1.84

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1264

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93-0

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16-0

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74-0

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0195

m11

246

79.9

8669

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4141

11.

8538

8617

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17.4

622

13.7

821

0.94

3-0

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0-0

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45-0

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0345

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3983

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96-6

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511.

8548

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15.8

640

4.63

160.

949

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86-0

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0-0

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50lm

0057

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589

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52-7

0.29

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1.85

5932

15.9

415

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1240

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70.

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32-0

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78.7

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3424

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16.9

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68.8

260

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66-0

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0551

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9176

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1.85

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15.5

215

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2187

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39-0

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30lm

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79.7

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71.

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7617

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17.6

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51.6

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93m

1000

279

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87-6

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1.86

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5324

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0424

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75.1

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1.80

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40m

1208

383

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1-6

6.32

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1.86

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17.2

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1820

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20.

976

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15.9

315

82.7

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58-0

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l136

3181

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29-6

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1.86

3346

16.8

316

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2216

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10.

879

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53-0

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23-0

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40lm

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k615

676

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84-6

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1.86

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1154

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969

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27m

1237

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73m

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78.5

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0540

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73.4

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30lm

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84-6

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1.87

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16.9

116

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1661

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913

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57-0

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26-0

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60lm

0550

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93-0

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10lm

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25m

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3383

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93m

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0-0

.011

0.00

30lm

0175

m19

864

76.6

5556

-68.

4602

91.

9465

9116

.35

16.0

136

1.86

580.

982

-0.0

16-0

.035

-0.0

080

-0.0

22-0

.0lm

0184

k175

9976

.655

75-6

8.46

017

1.94

6593

16.4

316

.19

2185

.858

20.

976

-0.0

23-0

.037

-0.0

1-0

.024

0.0

lm02

87k5

453*

73.2

6482

-67.

3371

41.

9466

2216

.78

16.5

518

51.5

814

0.92

7-0

.008

0-0

.095

-0.0

010

-0.0

350.

0020

lm03

45k1

1158

83.6

8483

-67.

0275

51.

9469

1215

.29

15.0

639

8.77

370.

872

-0.0

49-0

.173

-0.0

19-0

.076

0.0

lm03

62n1

8001

*86

.561

98-6

6.88

331

1.95

0688

17.3

217

.31

1125

.682

60.

978

-0.0

040

-0.0

23-0

.002

0-0

.001

0-0

.0lm

0331

l193

8281

.996

02-6

6.52

695

1.95

1358

15.8

715

.63

837.

7715

0.90

4-0

.052

-0.1

39-0

.02

-0.0

590.

0010

170


0107

n205

3577

.441

38-7

0.40

098

1.95

3697

17.2

617

.07

1442

.794

00.

959

-0.0

12-0

.029

-0.0

080

-0.0

160.

0050

lm00

33m

2217

785

.459

51-6

9.53

269

1.95

4291

15.6

715

.66

1079

.823

80.

939

-0.0

030

-0.0

74-0

.001

0-0

.041

-0.0

010

lm03

14n5

827*

77.8

8079

-67.

1447

1.95

5694

16.9

916

.78

1898

.598

60.

967

-0.0

070

-0.0

5-0

.002

0-0

.033

0.0

lm00

32l1

2916

83.9

4649

-69.

6421

81.

9604

5915

.77

15.6

620

26.5

388

0.98

-0.0

15-0

.038

-0.0

050

-0.0

270.

0020

lm01

91n9

387*

80.2

9841

-67.

9263

61.

9627

516

.74

16.4

479

9.83

490.

957

0.01

1-0

.097

-0.0

040

-0.0

790.

0010

lm00

30k1

2130

*84

.071

57-6

9.13

973

1.96

284

17.0

817

.00

2063

.491

40.

959

-0.0

020

-0.0

76-0

.002

0-0

.055

-0.0

010

lm00

24m

7851

82.3

537

-69.

8022

11.

9662

6817

.28

17.2

322

43.6

361

0.89

90.

0060

-0.1

530.

0030

-0.1

020.

0lm

0170

l146

5174

.949

12-6

7.89

419

1.96

7818

17.6

017

.50

2334

.573

60.

935

-0.0

19-0

.101

-0.0

090

-0.0

27-0

.004

0lm

0294

n623

0*74

.468

89-6

7.14

491

1.96

9417

.02

16.8

515

27.5

936

0.99

3-0

.001

0-0

.019

-0.0

040

-0.0

160.

0030

lm01

23k1

2359

73.0

1024

-69.

4713

81.

9695

7415

.85

15.6

922

51.7

679

0.97

7-0

.005

0-0

.018

-0.0

020

-0.0

040

0.00

20lm

0165

l188

86*

74.2

6136

-68.

6112

41.

9747

9417

.35

17.3

415

32.5

938

0.89

4-0

.003

0-0

.145

-0.0

030

-0.0

570.

0010

lm00

91m

3031

679

.316

3-6

9.22

21.

9787

6116

.83

16.7

853

0.55

690.

928

-0.0

42-0

.105

-0.0

21-0

.052

0.00

10lm

0090

l129

95*

78.0

6702

-69.

2912

21.

9823

4216

.86

16.7

817

55.8

747

0.93

20.

0070

-0.0

530.

0030

-0.0

150.

0030

lm03

20l2

2546

*79

.329

81-6

6.55

835

1.98

4791

516

.37

16.1

321

83.7

525

0.92

6-0

.066

-0.1

16-0

.025

-0.0

67-0

.009

0lm

0020

k121

15*

81.9

8923

-69.

1416

91.

9894

755

14.4

014

.14

506.

5490

0.97

2-0

.013

-0.0

27-0

.002

0-0

.009

00.

0030

lm01

01n2

3916

*77

.416

95-6

9.34

105

1.99

006

14.6

214

.32

1154

.812

90.

863

-0.0

19-0

.184

-0.0

030

-0.0

720.

0070

lm00

25n1

5353

*83

.669

55-6

9.98

922

1.99

0814

16.6

316

.40

1916

.594

40.

972

-0.0

14-0

.029

-0.0

030

-0.0

0.00

10lm

0031

n230

92*

85.4

9733

-69.

3481

52.

0188

3217

.28

17.1

713

75.9

103

0.96

10.

0050

-0.0

460.

0010

-0.0

150.

0010

lm00

15n1

0153

*81

.448

54-6

9.95

987

2.02

0196

17.2

417

.20

1396

.903

60.

987

0.0

-0.0

180.

0-0

.01

0.00

10lm

0344

l255

1882

.610

61-6

7.28

287

2.02

3458

16.5

816

.42

2027

.573

90.

915

-0.0

66-0

.125

-0.0

27-0

.074

-0.0

050

lm05

83k6

016

82.4

9748

-70.

8483

22.

0243

8916

.20

15.9

914

75.7

354

0.97

5-0

.012

-0.0

36-0

.008

0-0

.024

-0.0

010

lm03

06l8

041*

75.7

7498

-67.

5026

22.

0253

776

17.6

017

.43

1821

.750

30.

972

-0.0

-0.0

40.

0030

-0.0

30.

0030

lm02

83n2

4858

73.3

6237

-66.

9084

32.

0261

0216

.43

16.2

718

19.6

920

0.97

6-0

.021

-0.0

47-0

.01

-0.0

320.

0020

lm05

61l1

5749

78.0

7403

-70.

6912

22.

0287

6417

.39

17.2

818

54.6

210

0.94

60.

0060

-0.0

580.

0030

-0.0

-0.0

010

lm03

66l1

5212

86.1

8124

-67.

5631

2.02

9431

15.7

215

.48

2033

.544

70.

973

-0.0

14-0

.034

-0.0

030

-0.0

010

0.00

30lm

0551

n105

0376

.505

45-7

0.66

306

2.03

144

15.8

515

.58

1881

.617

10.

991

-0.0

11-0

.012

0.0

-0.0

010

0.00

30lm

0323

l287

4179

.892

95-6

6.92

704

2.03

2993

17.5

017

.45

2344

.612

91.

003

-0.0

2-0

.034

-0.0

020

-0.0

25-0

.0lm

0632

l146

3792

.275

26-7

1.08

018

2.03

3454

16.5

016

.67

384.

7207

0.96

5-0

.021

-0.0

42-0

.009

0-0

.014

0.00

20lm

0307

l175

4276

.760

1-6

7.58

324

2.03

4164

15.6

415

.33

1628

.528

00.

99-0

.01

-0.0

17-0

.0-0

.0-0

.0lm

0386

l175

76*

89.9

2579

-67.

6368

12.

0417

117

.96

17.7

815

68.7

252

0.91

60.

011

-0.1

330.

0010

-0.1

03-0

.01

lm01

21l2

2166

72.9

5621

-69.

3845

62.

0424

4214

.94

14.9

721

30.7

894

0.98

6-0

.002

0-0

.016

-0.0

020

-0.0

1-0

.0lm

0310

n185

7478

.059

85-6

6.54

982.

0437

4316

.92

16.7

911

29.6

499

0.98

6-0

.019

-0.0

17-0

.001

0-0

.001

00.

0020

lm00

33k1

1169

85.0

617

-69.

4663

72.

0439

6315

.32

15.1

413

81.9

065

0.87

2-0

.038

-0.1

79-0

.013

-0.0

780.

0010

lm02

96m

1445

874

.261

1-6

7.39

555

2.04

4072

15.5

015

.30

2198

.628

00.

923

-0.0

3-0

.091

-0.0

060

-0.0

260.

0050

lm03

23k3

395

80.0

2339

-66.

6192

32.

0466

9417

.04

17.1

222

24.7

712

0.93

1-0

.049

-0.1

23-0

.027

-0.0

75-0

.001

0lm

0394

m95

36*

92.0

4965

-67.

0156

32.

0480

4416

.82

16.6

121

40.8

873

0.94

0.00

30-0

.119

0.00

40-0

.096

-0.0

010

lm04

27n1

2788

*76

.053

93-6

6.15

369

2.04

8492

17.7

717

.66

1764

.841

50.

95-0

.003

0-0

.061

-0.0

010

-0.0

370.

0040

lm01

84n1

1334

77.1

8704

-68.

5739

12.

0488

4517

.19

17.0

318

92.8

390

0.93

40.

0010

-0.0

98-0

.009

0-0

.066

-0.0

020

lm01

81l1

5831

77.9

7285

-67.

8912

62.

0499

6516

.44

16.2

510

91.7

610

0.93

8-0

.026

-0.0

63-0

.005

0-0

.012

0.00

30lm

0177

l228

2176

.204

12-6

9.01

093

2.05

0346

16.3

816

.07

403.

7508

0.95

8-0

.013

-0.0

53-0

.012

-0.0

320.

0030

lm03

23k1

6171

80.1

1238

-66.

6972

82.

0509

6417

.04

16.9

643

4.75

520.

903

-0.1

02-0

.141

-0.0

4-0

.076

0.00

30

171

lm02

07k2

7793

*81

.773

97-6

8.87

582.

0549

9417

.11

16.9

419

55.6

861

0.93

7-0

.013

-0.0

59-0

.002

0-0

.012

0.00

10lm

0214

l232

5782

.606

28-6

8.65

832.

0565

0517

.55

17.4

221

30.8

364

0.96

5-0

.023

-0.0

4-0

.009

0-0

.034

0.00

60lm

0454

l249

5679

.677

53-6

5.88

205

2.05

7119

16.4

616

.26

1109

.817

70.

985

-0.0

14-0

.026

-0.0

1-0

.019

0.00

10lm

0467

m13

027*

82.4

3788

-65.

9909

92.

0578

661

16.3

616

.13

1977

.644

60.

925

0.00

30-0

.089

-0.0

020

-0.0

32-0

.002

0lm

0030

l128

6684

.005

75-6

9.29

671

2.05

8756

15.6

915

.62

2223

.628

80.

948

-0.0

27-0

.065

-0.0

070

-0.0

2-0

.001

0lm

0101

m21

049

77.6

1272

-69.

1768

62.

0591

9815

.91

15.7

520

93.9

045

0.92

5-0

.014

-0.0

87-0

.005

0-0

.014

-0.0

050

lm02

17n1

1196

83.9

752

-68.

9330

82.

0592

6516

.00

15.7

811

97.6

603

0.99

2-0

.007

0-0

.014

-0.0

010

-0.0

050

-0.0

010

lm00

31l2

6732

85.0

0806

-69.

3696

62.

0607

8717

.38

17.3

515

81.6

987

0.97

7-0

.007

0-0

.081

-0.0

020

-0.0

69-0

.009

0lm

0346

m26

007*

83.1

9507

-67.

4804

2.06

2730

116

.92

16.7

519

52.6

230

0.90

9-0

.001

0-0

.138

-0.0

090

-0.0

820.

0lm

0347

m24

253

84.1

2629

-67.

4671

2.06

2809

16.8

416

.64

1618

.682

10.

984

-0.0

1-0

.045

-0.0

090

-0.0

250.

0030

lm00

15m

3337

0*81

.495

03-6

9.92

983

2.06

4046

16.7

116

.46

775.

8333

0.87

3-0

.004

0-0

.166

0.00

10-0

.058

0.00

10lm

0581

l215

36*

82.6

2171

-70.

7256

22.

0641

1617

.37

17.2

219

01.8

440

0.96

-0.0

23-0

.096

-0.0

080

-0.0

81-0

.003

0lm

0021

l660

983

.013

33-6

9.24

357

2.06

4204

15.8

015

.57

384.

7892

0.87

7-0

.058

-0.1

56-0

.022

-0.0

760.

0060

lm01

03n1

9330

*77

.574

42-6

9.65

899

2.06

4678

16.7

816

.51

2185

.653

20.

981

0.01

3-0

.051

0.00

50-0

.038

-0.0

010

lm01

82k1

6150

*76

.836

47-6

8.12

493

2.06

5838

16.3

116

.18

2227

.610

90.

991

-0.0

020

-0.0

380.

0070

-0.0

090

-0.0

020

lm03

40m

1595

082

.986

13-6

6.35

673

2.06

6753

15.7

815

.54

402.

6230

0.98

9-0

.009

0-0

.021

-0.0

050

-0.0

070

-0.0

lm02

94k3

0560

73.8

5571

-67.

0603

82.

0669

5916

.48

16.4

011

50.6

036

0.98

20.

0020

-0.0

54-0

.002

0-0

.039

-0.0

13lm

0606

m11

871

86.4

4399

-71.

5754

72.

0718

4717

.05

16.9

617

52.8

762

0.97

4-0

.025

-0.0

30.

00.

0030

0.0

lm00

13k3

0220

*81

.044

65-6

9.56

256

2.07

2228

17.1

417

.15

2218

.845

20.

972

0.00

40-0

.071

-0.0

050

-0.0

59-0

.001

0lm

0030

k163

4284

.145

84-6

9.17

465

2.07

2852

16.2

516

.14

2225

.702

20.

963

-0.0

21-0

.077

-0.0

070

-0.0

6-0

.006

0lm

0344

m10

932

83.2

9023

-67.

0270

52.

0773

7115

.94

15.7

117

76.8

603

0.98

-0.0

080

-0.0

23-0

.004

0-0

.008

00.

0020

lm00

30n2

0233

84.2

28-6

9.38

287

2.07

7922

15.9

115

.78

2141

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50.

99-0

.006

0-0

.021

0.0

-0.0

070

-0.0

010

lm05

87l1

8183

*82

.605

52-7

1.78

322

2.07

7996

16.7

016

.59

1277

.548

10.

972

0.00

30-0

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0.00

20-0

.006

0-0

.0lm

0364

n128

0286

.753

11-6

7.19

625

2.07

8818

16.8

416

.67

1336

.476

30.

909

0.00

40-0

.14

0.00

10-0

.077

-0.0

020

lm01

20n2

8365

72.6

6602

-69.

3786

42.

0793

1516

.75

16.6

110

90.6

622

0.97

1-0

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0-0

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-0.0

050

-0.0

140.

0060

lm03

20n1

1672

79.7

1178

-66.

4789

32.

0822

4717

.40

17.2

718

34.7

450

0.97

9-0

.03

-0.0

23-0

.003

00.

0010

-0.0

040

lm03

76m

1986

188

.630

75-6

7.48

616

2.08

2899

16.8

416

.59

1910

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90.

985

0.00

60-0

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0.00

20-0

.025

-0.0

030

lm01

35k2

2834

71.1

4445

-69.

8975

22.

0860

7516

.83

16.7

714

04.7

858

0.95

5-0

.003

0-0

.072

-0.0

030

-0.0

37-0

.004

0lm

0216

l176

0282

.583

84-6

8.98

538

2.08

8156

16.0

915

.90

2155

.804

70.

94-0

.008

0-0

.107

-0.0

040

-0.0

790.

0030

lm02

83l8

947

73.2

4627

-66.

8092

82.

0882

2516

.07

15.9

025

75.5

757

0.94

1-0

.003

0-0

.085

-0.0

030

-0.0

560.

0030

lm03

53k1

3716

85.4

3765

-66.

6865

72.

0904

17.1

517

.04

2183

.806

10.

982

0.0

-0.0

37-0

.011

-0.0

190.

0090

lm03

74l1

5319

87.9

8088

-67.

2202

52.

0905

4716

.63

16.4

416

30.5

740

0.90

4-0

.055

-0.1

07-0

.024

-0.0

330.

01lm

0120

n118

1072

.364

81-6

9.27

577

2.09

0994

16.6

916

.56

1867

.564

60.

984

-0.0

1-0

.021

-0.0

030

-0.0

070

0.0

lm00

21n1

4065

83.6

9031

-69.

2812

52.

0919

7317

.16

17.0

181

8.81

440.

963

-0.0

12-0

.077

-0.0

010

-0.0

53-0

.007

0lm

0017

k186

80*

80.8

4479

-70.

2232

22.

0940

4817

.30

17.3

625

35.8

269

0.96

10.

0-0

.055

0.00

40-0

.025

-0.0

010

lm04

26n2

3242

*75

.023

46-6

6.21

718

2.09

473

16.6

716

.37

1982

.543

50.

944

-0.0

030

-0.0

80.

0020

-0.0

560.

0lm

0311

k116

3478

.245

1-6

6.33

708

2.09

5304

16.9

816

.74

1997

.551

00.

987

-0.0

090

-0.0

19-0

.001

0-0

.004

00.

0010

lm05

43m

1126

7*74

.621

18-7

0.85

887

2.09

621

16.8

916

.78

1291

.488

90.

876

-0.0

040

-0.1

7-0

.001

0-0

.077

0.00

20lm

0284

n240

9172

.427

96-6

7.28

827

2.09

8031

17.2

317

.15

1546

.747

40.

976

-0.0

29-0

.024

0.00

200.

0010

0.00

80lm

0120

n120

6472

.711

61-6

9.27

655

2.09

9324

17.0

716

.96

2344

.525

30.

928

-0.0

12-0

.067

-0.0

050

-0.0

030

-0.0

010

lm00

20k1

8818

81.9

151

-69.

1884

42.

1014

9115

.79

15.5

715

55.6

796

0.96

4-0

.002

0-0

.044

-0.0

020

-0.0

22-0

.0

172


0184

k771

476

.919

56-6

8.40

232

2.10

2557

15.4

115

.21

1842

.823

60.

977

-0.0

11-0

.021

0.00

10-0

.002

0-0

.003

0lm

0211

k229

00*

83.5

6939

-67.

7899

52.

1039

9817

.58

17.4

319

45.7

784

0.98

1-0

.009

0-0

.039

-0.0

040

-0.0

330.

0010

lm03

46n1

1026

83.2

7558

-67.

5331

62.

1082

7815

.35

15.0

920

53.5

015

0.97

4-0

.008

0-0

.046

-0.0

020

-0.0

350.

0lm

0121

n196

9773

.299

7-6

9.31

924

2.10

8675

17.2

317

.13

871.

5515

0.96

-0.0

090

-0.0

52-0

.001

0-0

.03

0.00

10lm

0090

n289

7778

.400

84-6

9.37

809

2.10

8725

16.4

516

.36

455.

8341

0.94

2-0

.026

-0.1

11-0

.014

-0.0

840.

0020

lm02

10n2

4868

82.9

734

-67.

9606

52.

1137

516

.60

16.4

014

70.6

691

0.93

6-0

.012

-0.0

880.

0030

-0.0

39-0

.004

0lm

0585

k286

782

.670

01-7

1.16

974

2.11

3799

17.3

317

.26

1566

.628

80.

945

-0.0

1-0

.058

-0.0

11-0

.016

0.00

30lm

0014

l168

0680

.071

67-7

0.01

212.

1162

7417

.35

17.1

914

42.8

081

0.91

50.

0090

-0.1

28-0

.006

0-0

.086

-0.0

040

lm01

84k2

7793

*76

.918

22-6

8.52

216

2.11

6352

17.4

717

.45

1749

.927

00.

948

-0.0

080

-0.0

65-0

.004

0-0

.013

-0.0

020

lm03

40l8

015

82.7

471

-66.

4597

62.

1178

6615

.86

15.6

510

75.7

470

0.95

7-0

.019

-0.0

520.

0-0

.009

00.

01lm

0447

m16

378

79.0

9147

-66.

0132

72.

1199

3816

.71

16.4

911

53.6

390

0.97

8-0

.011

-0.0

37-0

.01

-0.0

2-0

.003

0lm

0285

k419

373

.283

19-6

6.97

343

2.12

335

15.5

915

.46

1867

.570

20.

984

-0.0

16-0

.012

-0.0

040

-0.0

050

0.00

10lm

0345

k762

883

.437

81-6

7.00

561

2.12

3454

15.3

715

.18

1169

.796

50.

965

-0.0

050

-0.0

44-0

.002

0-0

.017

0.00

10lm

0111

k672

274

.884

13-6

9.08

629

2.12

4105

17.0

516

.86

1374

.888

70.

953

-0.0

030

-0.0

630.

0020

-0.0

330.

0020

lm01

31m

1381

9*71

.702

55-6

9.13

283

2.12

4317

.22

17.0

821

95.6

001

0.91

40.

0020

-0.1

14-0

.002

0-0

.038

0.00

60lm

0020

l916

382

.077

43-6

9.26

829

2.12

7403

16.2

215

.96

1164

.721

20.

981

-0.0

21-0

.021

-0.0

-0.0

010

-0.0

010

lm01

64l8

885

73.0

8891

-68.

5636

42.

1294

6917

.09

16.9

622

45.7

783

0.97

6-0

.013

-0.0

37-0

.004

0-0

.013

0.00

10lm

0831

m87

3886

.437

87-7

3.42

908

2.13

2923

17.3

517

.38

1920

.786

50.

931

-0.0

050

-0.1

01-0

.004

0-0

.051

0.00

30lm

0214

k135

9082

.360

9-6

8.43

753

2.13

3649

17.2

117

.14

950.

4813

0.96

5-0

.023

-0.0

250.

0020

0.00

30-0

.0lm

0164

m11

674

73.6

4248

-68.

4231

72.

1361

617

.16

17.0

622

14.6

954

0.94

3-0

.005

0-0

.07

0.00

10-0

.025

0.00

20lm

0327

m55

6280

.564

02-6

7.33

692.

1370

4616

.20

15.9

414

23.8

485

0.97

-0.0

16-0

.026

-0.0

-0.0

010

0.00

20lm

0557

n520

876

.487

16-7

1.68

366

2.13

7119

15.5

315

.16

2251

.633

70.

949

-0.0

020

-0.0

68-0

.002

0-0

.028

0.00

10lm

0335

n145

4282

.378

6-6

7.18

996

2.13

9656

17.2

116

.97

1751

.858

20.

946

-0.0

090

-0.0

94-0

.007

0-0

.071

-0.0

090

lm00

93n2

2090

*79

.416

49-6

9.67

019

2.14

0468

17.5

517

.57

1622

.544

20.

975

-0.0

040

-0.0

40.

0080

-0.0

35-0

.0lm

0574

m16

657

79.9

4568

-71.

2485

42.

1407

5615

.98

15.8

219

30.6

592

0.93

9-0

.02

-0.0

95-0

.011

-0.0

70.

0lm

0157

m11

115

72.8

539

-68.

7723

82.

1417

617

.16

16.9

923

30.5

523

0.94

8-0

.026

-0.0

52-0

.006

0-0

.012

-0.0

020

lm01

15k2

3126

74.8

9513

-69.

8848

92.

1422

1817

.25

17.2

213

81.9

210

0.98

2-0

.003

0-0

.05

0.00

20-0

.038

-0.0

030

lm03

64k5

553

86.2

3784

-66.

9894

82.

1438

2116

.65

16.4

922

45.8

514

0.98

9-0

.016

-0.0

140.

0010

0.0

-0.0

010

lm03

17k3

682

78.4

3808

-67.

3299

12.

1452

3916

.24

15.9

722

57.6

240

0.95

6-0

.011

-0.0

63-0

.007

0-0

.041

0.00

70lm

0013

l323

6580

.913

83-6

9.72

612.

1457

5516

.15

16.1

838

0.70

201.

025

-0.0

020

-0.0

28-0

.001

0-0

.026

-0.0

020

lm02

80n2

3309

72.7

8232

-66.

5674

22.

1464

0816

.90

16.7

417

68.7

941

0.94

4-0

.035

-0.0

59-0

.008

0-0

.017

0.00

20lm

0031

l948

0*84

.971

1-6

9.25

849

2.14

9394

17.1

017

.26

2206

.656

50.

97-0

.001

0-0

.063

-0.0

060

-0.0

22-0

.005

0lm

0365

l953

287

.078

31-6

7.16

921

2.14

9591

17.3

717

.26

1076

.849

70.

914

-0.0

98-0

.131

-0.0

46-0

.087

0.00

10lm

0354

l792

384

.426

79-6

7.15

897

2.14

9846

17.2

317

.07

1078

.871

10.

998

-0.0

32-0

.024

-0.0

21-0

.017

0.00

40lm

0331

m11

496

82.3

5971

-66.

3166

42.

1514

7315

.98

15.6

794

7.50

960.

967

-0.0

15-0

.026

0.00

10-0

.001

00.

0040

lm01

84k1

2216

76.6

4318

-68.

4287

22.

1544

7515

.51

15.1

912

81.5

396

0.94

20.

0020

-0.0

9-0

.006

0-0

.054

-0.0

010

lm01

75m

1431

076

.642

87-6

8.42

884

2.15

4499

15.1

914

.95

351.

8527

0.97

1-0

.003

0-0

.08

0.00

40-0

.064

-0.0

080

lm02

85m

2081

773

.351

47-6

7.08

557

2.15

5777

16.2

416

.18

1619

.530

50.

986

-0.0

090

-0.0

27-0

.005

0-0

.022

-0.0

020

lm01

12n2

0997

74.4

3411

-69.

7480

82.

1565

0316

.45

16.3

242

8.62

440.

942

-0.0

25-0

.068

-0.0

060

-0.0

190.

0030

lm02

04k1

1078

*80

.589

88-6

8.41

759

2.15

745

16.9

116

.90

327.

8730

0.98

1-0

.004

0-0

.026

-0.0

030

-0.0

110.

0010

lm00

25n2

2937

83.3

5719

-70.

0313

82.

1578

7415

.35

15.1

922

33.5

777

0.99

5-0

.013

-0.0

070

-0.0

010

-0.0

010

-0.0

173

lm03

75k1

9793

88.8

2509

-67.

0947

92.

1586

9116

.43

16.3

016

41.5

539

0.93

1-0

.005

0-0

.078

-0.0

030

-0.0

18-0

.002

0lm

0016

n213

06*

80.6

1341

-70.

3948

2.15

9334

17.0

016

.83

1763

.805

80.

883

-0.0

81-0

.172

-0.0

43-0

.092

-0.0

020

lm03

77m

4439

89.3

4411

-67.

3373

12.

1603

3517

.52

17.2

821

98.7

009

0.96

4-0

.043

-0.0

52-0

.003

0-0

.013

-0.0

020

lm00

14m

1670

080

.303

62-6

9.84

745

2.16

0507

17.3

417

.26

1771

.884

10.

945

-0.0

080

-0.0

87-0

.012

-0.0

67-0

.003

0lm

0344

k168

5482

.613

13-6

7.06

915

2.16

4252

16.0

015

.81

533.

5582

0.96

6-0

.009

0-0

.077

-0.0

030

-0.0

580.

0030

lm00

31m

1900

185

.263

59-6

9.17

275

2.16

5249

17.1

917

.32

1150

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30.

954

-0.0

34-0

.08

-0.0

080

-0.0

26-0

.01

lm03

21m

8452

80.6

0069

-66.

2937

52.

1682

2116

.88

16.5

581

9.82

270.

974

-0.0

17-0

.027

0.0

-0.0

010

-0.0

010

lm03

17k5

360

78.5

1571

-67.

3418

32.

1697

1615

.68

15.4

578

6.83

200.

984

-0.0

090

-0.0

16-0

.003

0-0

.007

00.

0040

lm01

22m

5050

*72

.741

68-6

9.43

543

2.16

9742

16.3

616

.15

2172

.692

20.

966

-0.0

16-0

.067

-0.0

1-0

.047

-0.0

010

lm04

76n8

386*

83.5

0353

-66.

1080

62.

1700

301

17.2

117

.07

2236

.603

00.

886

-0.0

070

-0.1

490.

0040

-0.0

640.

0060

lm02

14n1

0775

*82

.998

-68.

5720

92.

1757

2817

.39

17.2

311

66.6

841

0.98

2-0

.015

-0.0

28-0

.01

-0.0

230.

0020

lm01

04k1

0462

76.1

6645

-69.

8147

72.

1780

2816

.43

16.2

213

67.8

576

0.88

2-0

.016

-0.1

7-0

.003

0-0

.088

-0.0

040

lm00

12m

1679

880

.647

25-6

9.52

878

2.18

3354

15.8

415

.48

697.

8926

0.93

6-0

.02

-0.0

95-0

.015

-0.0

59-0

.002

0lm

0205

n257

4282

.169

42-6

8.69

351

2.18

4881

15.3

514

.97

1136

.851

10.

964

-0.0

050

-0.0

57-0

.011

-0.0

27-0

.0lm

0294

n133

8874

.436

11-6

7.18

884

2.18

8141

15.6

915

.44

1858

.828

20.

983

-0.0

-0.0

21-0

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-0.0

080

-0.0

070

lm03

66l6

375*

86.1

5242

-67.

4924

72.

1890

061

17.1

517

.00

2155

.848

70.

974

-0.0

070

-0.0

38-0

.006

0-0

.019

-0.0

030

lm05

43m

9484

*74

.378

11-7

0.85

007

2.18

9417

.29

17.1

386

4.69

090.

975

-0.0

-0.0

460.

0010

-0.0

38-0

.001

0lm

0315

m20

618*

78.8

6678

-67.

0694

52.

1919

517

.34

17.1

513

89.8

800

0.97

-0.0

060

-0.0

27-0

.003

0-0

.009

00.

0010

lm01

13m

6637

*75

.318

89-6

9.43

376

2.19

245

17.0

016

.88

1830

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10.

971

-0.0

040

-0.0

26-0

.001

0-0

.009

0-0

.003

0lm

0461

n156

4082

.522

2-6

5.17

632.

1925

4617

.34

17.1

214

45.8

946

0.97

4-0

.007

0-0

.031

-0.0

030

-0.0

120.

0020

lm01

91n2

265

79.9

646

-67.

8349

12.

1932

4117

.04

16.9

019

00.7

488

0.95

3-0

.015

-0.0

66-0

.008

0-0

.041

0.00

20lm

0013

m20

283

81.5

1292

-69.

5146

2.19

3383

15.3

915

.13

2255

.652

30.

969

-0.0

15-0

.034

0.0

0.0

0.0

lm01

23k1

5744

72.8

1945

-69.

4915

52.

1957

7416

.50

16.3

410

90.6

622

0.98

9-0

.031

-0.0

16-0

.009

0-0

.016

0.00

10lm

0541

n498

174

.665

65-7

0.64

066

2.19

5876

16.8

316

.48

1775

.772

00.

984

-0.0

16-0

.022

-0.0

070

-0.0

130.

0020

lm00

44n5

926

86.5

9323

-69.

9439

32.

1980

316

.92

16.9

120

17.5

920

0.88

6-0

.098

-0.1

57-0

.044

-0.0

820.

0070

lm02

81n1

4618

73.5

6365

-66.

4911

62.

1997

8617

.07

16.8

715

26.5

916

0.88

9-0

.087

-0.1

81-0

.048

-0.1

080.

0060

lm03

00m

2557

176

.144

99-6

6.41

666

2.20

0747

15.9

415

.64

1825

.702

80.

94-0

.021

-0.0

59-0

.002

0-0

.009

00.

0030

lm03

40m

1956

883

.179

12-6

6.38

233

2.20

2876

17.4

917

.25

1803

.869

20.

968

-0.0

17-0

.042

-0.0

11-0

.024

0.0

lm02

90n1

2262

74.3

59-6

6.48

642

2.20

3112

16.3

716

.21

1181

.647

00.

948

-0.0

090

-0.0

99-0

.009

0-0

.075

0.00

40lm

0370

k175

1287

.812

32-6

6.37

514

2.20

7377

17.0

716

.89

1524

.688

10.

887

-0.0

74-0

.145

-0.0

31-0

.065

0.00

40lm

0107

k229

8577

.271

91-7

0.24

754

2.20

7411

17.3

217

.09

435.

7162

0.98

0.00

50-0

.036

0.00

10-0

.024

-0.0

020

lm02

90l2

1965

73.9

6035

-66.

5757

72.

2112

9215

.93

15.8

531

7.85

960.

989

-0.0

040

-0.0

12-0

.001

0-0

.006

0-0

.003

0lm

0241

l253

9089

.188

69-6

7.97

323

2.21

4714

17.4

417

.34

365.

7348

0.97

8-0

.006

0-0

.03

-0.0

050

-0.0

210.

0010

lm06

10k4

113

87.8

5881

-70.

5359

2.21

4823

17.1

516

.98

1244

.682

30.

975

0.00

20-0

.039

-0.0

010

-0.0

29-0

.0lm

0591

n253

1485

.290

76-7

0.74

622.

2168

8716

.04

15.8

411

67.8

282

0.92

9-0

.03

-0.0

81-0

.009

0-0

.022

0.00

20lm

0220

k199

6184

.459

12-6

7.79

554

2.21

799

17.0

016

.84

2297

.769

70.

905

-0.0

69-0

.133

-0.0

28-0

.069

-0.0

040

lm00

20k1

1440

82.0

627

-69.

1366

12.

2201

6915

.22

14.9

318

69.6

092

0.97

5-0

.009

0-0

.063

-0.0

070

-0.0

46-0

.002

0lm

0203

n153

9381

.844

17-6

8.23

549

2.22

5954

15.5

215

.28

394.

7756

0.97

3-0

.012

-0.0

250.

0010

0.0

0.00

30lm

0581

k693

182

.646

45-7

0.48

988

2.22

7595

17.0

716

.87

1879

.640

20.

978

-0.0

2-0

.019

-0.0

010

-0.0

020

0.00

60lm

0230

m41

5586

.841

93-6

7.67

424

2.22

9129

17.1

616

.89

2019

.582

10.

974

-0.0

030

-0.0

52-0

.013

-0.0

27-0

.013

lm00

33m

2476

285

.328

05-6

9.54

912

2.23

0059

16.3

116

.16

837.

7160

0.98

6-0

.006

0-0

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-0.0

020

-0.0

21-0

.001

0

174


0285

n464

573

.581

79-6

7.13

282.

2307

5517

.20

16.9

822

25.5

834

0.98

1-0

.012

-0.0

24-0

.005

0-0

.015

0.00

10lm

0303

n124

0376

.834

86-6

6.82

148

2.23

4478

16.6

916

.53

1860

.581

60.

944

-0.0

070

-0.0

85-0

.003

0-0

.052

0.00

10lm

0335

k267

6081

.739

43-6

7.11

696

2.23

4913

16.2

216

.09

1117

.693

30.

887

-0.0

65-0

.149

-0.0

26-0

.068

0.00

10lm

0103

l113

1677

.230

53-6

9.61

654

2.23

5387

16.8

716

.78

1272

.554

10.

976

-0.0

14-0

.032

-0.0

060

-0.0

14-0

.004

0lm

0175

k257

2475

.997

16-6

8.49

432

2.24

1225

17.2

617

.22

1153

.601

50.

932

-0.0

37-0

.1-0

.016

-0.0

41-0

.002

0lm

0301

n983

276

.878

18-6

6.45

832

2.24

2879

16.1

615

.99

1895

.745

40.

984

-0.0

12-0

.018

-0.0

060

-0.0

11-0

.0lm

0127

n214

8773

.644

13-7

0.40

732

2.24

4659

17.1

116

.88

1341

.922

30.

965

0.00

20-0

.056

-0.0

010

-0.0

41-0

.002

0lm

0200

k250

3480

.532

84-6

7.81

569

2.24

4789

16.6

516

.21

1788

.813

20.

947

-0.0

19-0

.079

-0.0

1-0

.056

0.00

40lm

0193

m14

935

79.9

7507

-68.

0820

32.

2497

9715

.10

14.8

915

70.5

930

0.96

7-0

.017

-0.0

38-0

.001

0-0

.005

00.

0020

lm00

20k2

4295

82.1

302

-69.

2279

42.

2507

0116

.27

16.0

519

16.5

944

0.97

90.

0010

-0.0

270.

0010

-0.0

130.

0010

lm03

31l1

7455

81.9

9669

-66.

5146

62.

2549

8416

.95

16.9

319

34.7

177

0.96

3-0

.001

0-0

.053

-0.0

-0.0

34-0

.0lm

0466

l152

3981

.324

46-6

6.16

268

2.25

864

16.2

215

.99

2211

.763

80.

931

-0.0

16-0

.115

-0.0

1-0

.078

0.00

40lm

0021

l327

9183

.077

67-6

9.38

839

2.25

996

16.9

416

.78

1644

.552

70.

962

-0.0

040

-0.0

720.

0010

-0.0

470.

0010

lm00

33l8

128*

85.0

0657

-69.

6018

82.

2622

781

16.0

616

.26

1838

.843

10.

927

-0.0

16-0

.122

-0.0

080

-0.0

93-0

.004

0lm

0355

k331

785

.179

43-6

6.97

744

2.26

5278

17.3

817

.32

1850

.818

21.

004

-0.0

21-0

.012

0.00

40-0

.003

0-0

.01

lm01

17m

1058

475

.354

56-7

0.17

046

2.26

826

15.6

115

.36

1139

.841

70.

973

-0.0

14-0

.023

0.0

-0.0

-0.0

010

lm05

51n1

3003

76.5

5602

-70.

6779

2.27

0432

15.4

515

.11

1861

.659

40.

991

0.00

40-0

.025

-0.0

020

-0.0

20.

0lm

0294

m26

342

74.5

6661

-67.

1114

2.27

1254

17.1

116

.95

1867

.591

50.

992

-0.0

2-0

.014

-0.0

18-0

.008

0-0

.001

0lm

0100

n569

076

.657

27-6

9.23

942.

2732

116

.90

16.7

520

09.5

280

0.90

7-0

.009

0-0

.117

-0.0

020

-0.0

56-0

.001

0lm

0030

n182

0284

.494

21-6

9.32

818

2.27

3798

16.1

315

.97

1873

.745

00.

988

-0.0

18-0

.014

-0.0

040

-0.0

110.

0010

lm05

51k2

2031

75.9

421

-70.

6197

52.

2760

117

.29

17.1

720

14.5

141

0.95

8-0

.011

-0.0

48-0

.018

-0.0

3-0

.002

0lm

0093

m18

940

79.4

1344

-69.

5021

62.

2772

2116

.57

16.3

912

72.5

694

0.98

6-0

.012

-0.0

24-0

.006

0-0

.014

-0.0

lm01

23m

1204

673

.519

01-6

9.46

607

2.27

8014

16.0

515

.96

2172

.692

20.

913

-0.0

45-0

.106

-0.0

13-0

.04

0.00

50lm

0173

l139

8575

.927

25-6

8.23

103

2.27

859

16.2

116

.06

2208

.592

50.

968

-0.0

19-0

.025

0.0

0.00

100.

0030

lm00

92m

2011

7*78

.507

88-6

9.55

312

2.27

942

16.9

116

.83

2390

.524

40.

973

-0.0

080

-0.0

26-0

.003

0-0

.012

-0.0

020

lm03

54m

1836

784

.906

15-6

7.07

169

2.27

9477

16.8

416

.74

1952

.645

90.

962

-0.0

070

-0.0

48-0

.005

0-0

.008

00.

0lm

0161

m20

878

74.5

8093

-67.

7728

92.

2795

816

.52

16.3

087

9.55

200.

968

-0.0

020

-0.0

55-0

.0-0

.034

-0.0

010

lm06

81m

1607

377

.636

93-7

1.94

809

2.28

0521

17.3

917

.16

1503

.639

20.

945

0.00

60-0

.092

-0.0

020

-0.0

66-0

.0lm

0037

m13

144*

85.3

6341

-70.

1932

12.

2806

3217

.45

17.3

110

71.8

607

0.97

40.

0030

-0.0

60.

0010

-0.0

42-0

.001

0lm

0211

m23

264

83.9

8286

-67.

7886

12.

2809

8216

.35

16.1

111

50.7

130

0.89

-0.0

56-0

.146

-0.0

26-0

.067

0.00

20lm

0117

m15

641

75.5

9811

-70.

2015

12.

2838

16.3

016

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442.

7809

0.98

7-0

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0-0

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0.0

-0.0

10.

0030

lm01

75n3

1573

*76

.579

35-6

8.67

835

2.28

6902

15.9

315

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2030

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10.

993

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020

-0.0

13-0

.002

0-0

.008

0-0

.001

0lm

0543

n271

9574

.728

01-7

1.10

363

2.29

3317

17.2

517

.06

1289

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60.

962

-0.0

31-0

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0.0

0.00

100.

0010

lm01

84k1

3561

*76

.855

96-6

8.43

673

2.29

4172

16.5

816

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418.

8373

0.98

8-0

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17-0

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0-0

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020

lm02

94n1

0273

74.3

1829

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1699

52.

2989

0415

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15.5

622

39.7

894

0.93

1-0

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420.

0070

lm03

37k2

0128

81.9

1348

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4423

52.

3002

9815

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15.2

817

94.8

525

0.94

5-0

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99-0

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0-0

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0.0

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90l1

3156

78.1

5229

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2921

62.

3012

6616

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16.5

021

84.7

283

0.87

9-0

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53-0

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0-0

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lm03

55n1

2209

85.7

5128

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1831

42.

3037

9417

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17.1

513

83.8

643

0.92

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08-0

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420.

0040

lm03

13m

2134

878

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07-6

6.72

394

2.30

4919

15.6

315

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2545

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30.

958

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17-0

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040

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lm03

43l1

7247

83.7

9672

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8606

92.

3084

1117

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17.2

810

90.6

924

0.96

0.0

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62-0

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0-0

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010

lm03

22k2

0845

79.3

1416

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7731

42.

3115

4715

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15.7

589

2.62

130.

918

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4-0

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13-0

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0.00

30

175

lm05

86k1

6977

81.5

3131

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6079

82.

3161

0815

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14.9

915

56.7

363

0.97

90.

0030

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350.

0-0

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0.00

20lm

0166

k828

0*73

.303

92-6

8.75

893

2.32

533

16.8

816

.77

2229

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20.

946

-0.0

050

-0.0

64-0

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0-0

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0.00

10lm

0563

m21

591*

78.9

1696

-70.

9188

22.

3276

3217

.31

17.1

920

03.5

423

0.97

80.

0070

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37-0

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0-0

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060

lm03

66l2

1345

86.1

9773

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6337

2.32

8524

16.7

316

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1908

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60.

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26-0

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020

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070

0.0

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00l1

9491

80.4

8924

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9369

2.32

9272

15.9

315

.86

1993

.574

70.

938

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29-0

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020

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0.00

90lm

0592

n116

46*

84.1

8167

-71.

1173

12.

3295

3417

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16.9

717

75.7

456

0.97

30.

0010

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30.

0040

-0.0

1-0

.002

0lm

0096

n211

4778

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99-7

0.38

856

2.33

2835

17.1

516

.98

1914

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10.

922

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030

-0.1

19-0

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0.00

70lm

0186

n147

9077

.106

58-6

8.95

847

2.33

3025

17.1

117

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538.

5531

0.94

7-0

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58-0

.01

-0.0

190.

0010

lm00

30m

4163

84.3

7804

-69.

0881

72.

3334

1615

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15.3

138

8.84

960.

899

0.00

20-0

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270.

0060

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21l1

2322

73.1

6189

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3917

2.33

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16.8

216

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1482

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00.

971

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42-0

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0-0

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20k2

403*

82.1

265

-69.

0729

22.

3358

7217

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17.7

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7.50

880.

874

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770.

0030

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080.

01lm

0033

n254

4885

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3-6

9.70

678

2.34

0327

16.2

615

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1771

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10.

987

0.0

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6-0

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0-0

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010

lm01

15k2

8730

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18-6

9.91

555

2.34

1022

16.8

016

.76

1246

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20.

991

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050

-0.0

35-0

.001

0-0

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0.00

30lm

0211

k930

8*83

.447

62-6

7.70

132

2.34

1696

17.2

217

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1289

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10.

956

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11-0

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030

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130.

0020

lm01

86k5

622

76.9

543

-68.

7438

62.

3418

9816

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16.3

521

73.6

941

0.96

8-0

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0-0

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050

-0.0

22-0

.002

0lm

0033

l897

884

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57-6

9.60

731

2.34

4895

15.7

515

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2047

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20.

996

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090

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1-0

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0-0

.003

0-0

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0103

k404

377

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7-6

9.42

463

2.34

5441

15.8

915

.84

1224

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00.

974

-0.0

16-0

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-0.0

12-0

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0.00

70lm

0426

m23

482

75.0

7795

-66.

0628

42.

3455

7315

.15

14.8

314

47.7

508

0.95

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15-0

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-0.0

020

0.00

300.

0010

lm01

21l2

7892

73.2

1002

-69.

3667

82.

3460

417

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16.9

717

55.8

861

0.92

5-0

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0-0

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0.00

10-0

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040

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12l2

9182

74.1

3397

-69.

7355

82.

3473

8515

.57

15.3

825

74.6

019

0.95

20.

0040

-0.0

67-0

.0-0

.02

0.0

lm01

11n1

6405

75.4

7253

-69.

2932

42.

3479

7416

.90

16.7

715

39.6

904

0.96

6-0

.018

-0.0

26-0

.002

00.

0010

0.00

10lm

0364

n590

186

.491

51-6

7.14

732

2.34

7977

16.5

616

.51

374.

8669

0.91

3-0

.004

0-0

.101

0.00

20-0

.027

0.00

10lm

0437

n826

7*77

.381

03-6

6.11

499

2.35

3292

17.4

917

.33

2082

.923

60.

937

-0.0

030

-0.0

68-0

.002

0-0

.027

0.0

lm02

87n1

4280

*73

.571

27-6

7.55

517

2.35

3686

17.4

017

.15

1550

.625

20.

977

-0.0

030

-0.0

65-0

.003

0-0

.046

-0.0

010

lm02

23n3

0265

85.8

7513

-68.

3303

32.

3555

3115

.64

15.4

014

77.7

595

0.89

4-0

.035

-0.1

51-0

.018

-0.0

670.

0lm

0091

n165

2079

.310

01-6

9.29

892

2.36

1363

16.1

115

.91

1894

.611

10.

943

-0.0

3-0

.065

-0.0

050

-0.0

130.

0080

lm00

31m

1930

585

.283

77-6

9.17

464

2.36

1448

16.8

116

.83

1079

.823

80.

882

-0.0

67-0

.16

-0.0

33-0

.077

-0.0

lm02

94n9

088

74.4

3098

-67.

1626

82.

3656

8216

.87

16.7

512

73.4

985

0.88

-0.0

71-0

.161

-0.0

36-0

.079

0.00

20lm

0033

m29

238*

85.5

3677

-69.

5749

22.

3694

4217

.11

17.0

312

55.6

286

0.98

1-0

.004

0-0

.02

0.00

10-0

.015

-0.0

030

lm03

55n1

9896

*85

.675

14-6

7.23

285

2.37

175

17.3

917

.38

2239

.817

70.

980.

0-0

.024

0.0

-0.0

190.

0020

lm03

63m

3939

*87

.713

31-6

6.62

361

2.37

3044

17.9

717

.80

2317

.706

70.

969

-0.0

020

-0.0

4-0

.003

0-0

.025

-0.0

030

lm03

14n1

0346

77.7

4369

-67.

175

2.37

5213

15.3

515

.12

948.

4991

0.99

3-0

.004

0-0

.014

-0.0

040

-0.0

10.

0lm

0205

l592

881

.647

04-6

8.53

675

2.37

907

17.0

017

.00

1823

.808

60.

97-0

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-0.0

24-0

.001

00.

0-0

.001

0lm

0012

l245

72*

79.9

3726

-69.

7058

72.

3808

17.7

017

.55

2184

.752

10.

941

-0.0

080

-0.0

89-0

.005

0-0

.047

0.00

50lm

0120

l127

7272

.010

1-6

9.28

588

2.38

1339

16.7

516

.58

2186

.650

90.

983

-0.0

1-0

.022

-0.0

060

-0.0

12-0

.001

0lm

0367

m17

417*

87.3

9254

-67.

4282

72.

3814

6216

.60

16.4

615

81.7

108

0.97

70.

0060

-0.0

410.

0060

-0.0

390.

0010

lm05

41m

1720

174

.391

01-7

0.55

125

2.38

1813

16.3

416

.07

1924

.601

80.

92-0

.05

-0.1

15-0

.017

-0.0

440.

0010

lm04

27m

1691

576

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4-6

6.02

195

2.38

2868

17.3

717

.06

2191

.663

10.

97-0

.009

0-0

.049

-0.0

16-0

.026

0.00

70lm

0355

m83

9985

.750

41-6

7.00

582.

3843

416

.70

16.5

412

71.6

074

0.99

7-0

.01

-0.0

060

0.00

10-0

.001

0-0

.0lm

0035

n291

7485

.257

3-7

0.08

448

2.38

5178

15.8

415

.75

2225

.702

20.

944

-0.0

020

-0.1

14-0

.001

0-0

.078

-0.0

010

lm02

90m

1699

374

.308

85-6

6.42

699

2.38

6669

15.9

615

.78

2161

.732

30.

993

-0.0

090

-0.0

12-0

.003

0-0

.008

0-0

.001

0

176


0346

n107

3583

.110

24-6

7.53

125

2.38

7713

15.2

815

.06

1953

.749

20.

873

-0.0

36-0

.153

-0.0

19-0

.058

0.00

50lm

0354

l926

384

.533

28-6

7.16

815

2.38

8225

16.9

116

.78

1192

.738

60.

971

-0.0

27-0

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0.00

100.

0030

0.00

20lm

0557

l109

4576

.163

66-7

1.73

352.

3888

6617

.07

16.8

315

47.5

995

0.97

20.

0010

-0.0

64-0

.005

0-0

.045

0.00

70lm

0590

m35

0183

.994

41-7

0.50

731

2.38

9369

16.3

316

.09

2322

.675

40.

961

-0.0

19-0

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0.0

-0.0

020

-0.0

lm01

87l1

7648

78.0

774

-68.

9755

42.

3905

3217

.15

17.0

817

74.8

356

0.95

60.

0020

-0.0

68-0

.002

0-0

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-0.0

lm01

65l9

604

74.0

7694

-68.

5603

82.

3905

9917

.02

16.9

614

97.5

988

0.99

-0.0

2-0

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-0.0

020

-0.0

010

-0.0

030

lm02

97k1

6068

74.9

4967

-67.

4086

42.

3942

6715

.34

15.0

819

27.6

449

0.98

3-0

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0-0

.014

-0.0

010

0.00

100.

0010

lm00

15m

1296

4*81

.585

82-6

9.82

269

2.39

4782

17.3

817

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1198

.659

80.

964

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080

-0.0

490.

0040

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330.

0030

lm05

56k7

966

75.0

2718

-71.

5434

82.

3982

0816

.40

16.2

749

0.63

970.

984

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15-0

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-0.0

020

0.00

300.

0010

lm02

30l1

5982

86.0

8001

-67.

9137

22.

3983

5116

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16.7

413

16.5

454

0.97

0.00

30-0

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-0.0

050

-0.0

15-0

.003

0lm

0305

n139

6976

.924

68-6

7.22

035

2.39

9246

15.9

615

.75

2183

.700

20.

982

-0.0

090

-0.0

17-0

.001

0-0

.001

00.

0010

lm00

93m

6482

79.3

1403

-69.

4374

62.

4000

6817

.32

17.1

815

11.6

682

0.96

50.

0010

-0.0

58-0

.006

0-0

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0.00

40lm

0030

k742

184

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8-6

9.10

452.

4038

4216

.77

16.6

541

4.71

420.

963

-0.0

22-0

.05

-0.0

31-0

.02

-0.0

1lm

0344

n906

983

.375

07-6

7.16

455

2.40

841

17.0

516

.89

1500

.708

30.

917

0.00

30-0

.127

-0.0

070

-0.0

83-0

.002

0lm

0323

n207

98*

80.6

6736

-66.

8736

12.

4086

7217

.43

17.2

416

19.5

834

0.95

60.

0010

-0.0

76-0

.002

0-0

.06

0.00

60lm

0033

m27

772

85.3

8415

-69.

5671

32.

4112

1616

.64

16.5

522

39.6

372

0.98

7-0

.008

0-0

.017

-0.0

030

-0.0

110.

0010

lm02

90n7

998

74.3

7665

-66.

4562

22.

4130

3115

.78

15.9

079

2.78

800.

95-0

.02

-0.0

74-0

.014

-0.0

570.

0lm

0037

l456

384

.780

55-7

0.29

163

2.41

3848

17.2

917

.29

1186

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80.

972

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010

-0.0

5-0

.001

0-0

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0.00

10lm

0294

k281

42*

73.9

7016

-67.

1308

12.

4182

0216

.92

16.8

112

37.6

064

0.92

20.

0050

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290.

0030

-0.0

920.

0030

lm03

46k1

7136

82.6

852

-67.

4266

12.

4188

2415

.49

15.2

880

9.69

450.

931

0.00

10-0

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-0.0

020

-0.0

57-0

.001

0lm

0030

l158

1084

.018

83-6

9.31

956

2.41

9399

15.9

715

.99

1510

.698

60.

958

-0.0

12-0

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-0.0

080

-0.0

290.

0010

lm00

56l2

5826

87.9

5228

-70.

4338

32.

4199

8617

.17

16.9

419

17.8

619

0.90

80.

0010

-0.1

42-0

.006

0-0

.089

-0.0

040

lm01

57n1

5497

*72

.716

25-6

8.96

325

2.42

7398

17.1

717

.13

1792

.747

60.

985

0.00

10-0

.024

0.0

-0.0

150.

0lm

0015

n174

9981

.723

12-6

9.99

707

2.43

1098

16.8

716

.74

1530

.694

10.

931

-0.0

020

-0.1

03-0

.002

0-0

.066

-0.0

010

lm03

25m

1962

5*80

.366

54-6

7.07

111

2.43

1928

15.9

415

.71

800.

6959

0.98

9-0

.003

0-0

.02

-0.0

010

-0.0

18-0

.001

0lm

0105

l166

4076

.992

86-7

0.07

014

2.43

3279

17.1

016

.98

1212

.610

00.

986

0.0

-0.0

250.

0010

-0.0

14-0

.003

0lm

0345

m84

9083

.841

36-6

7.00

352

2.43

4907

15.7

015

.41

1815

.812

00.

943

-0.0

050

-0.1

-0.0

050

-0.0

66-0

.001

0lm

0325

n971

880

.643

54-6

7.15

893

2.43

6797

16.7

216

.55

1858

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00.

989

-0.0

040

-0.0

19-0

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0-0

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-0.0

010

lm00

13n2

2558

81.2

643

-69.

6749

82.

4374

4516

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16.1

485

7.76

050.

941

-0.0

36-0

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-0.0

050

-0.0

060

0.00

30lm

0344

l183

5782

.701

44-6

7.23

384

2.44

2181

16.6

016

.41

1940

.766

20.

98-0

.02

-0.0

35-0

.02

-0.0

26-0

.002

0lm

0550

m23

266

75.5

8039

-70.

6071

2.44

3675

15.4

415

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835.

6237

0.94

70.

0060

-0.0

660.

0020

-0.0

20.

0lm

0340

l229

6382

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49-6

6.57

868

2.44

7199

15.9

515

.74

1148

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60.

931

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-0.1

02-0

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0-0

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lm03

31n5

533

82.1

1053

-66.

4860

62.

4485

815

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15.6

470

1.79

000.

989

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090

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18-0

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0-0

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0lm

0035

k582

685

.176

19-6

9.79

019

2.45

7281

16.1

516

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1483

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00.

972

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17-0

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16-0

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030

lm05

51n5

128*

76.7

0335

-70.

7428

12.

4577

1217

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17.4

584

2.68

090.

963

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050

-0.0

59-0

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-0.0

220.

0020

lm01

65l1

4067

74.1

9318

-68.

5846

82.

4578

8816

.57

16.4

322

63.6

042

0.94

6-0

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67-0

.006

0-0

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0.00

20lm

0374

n649

988

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15-6

7.14

809

2.45

9114

17.1

116

.93

2057

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70.

984

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080

-0.0

28-0

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210.

0lm

0345

m13

290

84.1

0019

-67.

0321

22.

4605

516

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15.7

810

77.8

037

0.96

9-0

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43-0

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260.

0lm

0120

l224

3772

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19-6

9.35

882.

4651

4816

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16.4

321

91.6

165

0.96

3-0

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0-0

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040

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090

0.00

10lm

0344

k506

882

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2-6

6.98

962.

4656

0816

.30

16.1

416

18.6

821

0.98

1-0

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0-0

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14-0

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0.00

80lm

0343

l280

1983

.619

52-6

6.93

72.

4675

9616

.55

16.3

712

54.6

180

0.98

6-0

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24-0

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0-0

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0.00

40

177

lm02

85l2

5392

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53-6

7.27

032.

4683

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16.0

615

46.7

474

0.97

8-0

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0-0

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030

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170.

0020

lm02

13k2

4315

83.4

129

-68.

1394

62.

4694

9616

.87

16.8

118

83.6

801

0.95

0.00

20-0

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010

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50.

0040

lm00

93m

4296

79.4

8343

-69.

4247

32.

4699

8116

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16.1

357

4.50

170.

888

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64-0

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31-0

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0.00

10lm

0545

m66

9974

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74-7

1.18

265

2.47

1238

16.9

016

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1775

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00.

904

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13-0

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030

-0.0

39-0

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0lm

0024

l508

382

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3-6

9.94

233

2.47

1267

16.5

316

.44

2225

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50.

917

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63-0

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22-0

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0.00

30lm

0406

l944

*93

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33-6

7.49

614

2.47

3836

17.3

517

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1641

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00.

916

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050

-0.1

02-0

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0-0

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0.00

30lm

0095

m32

814

79.4

9724

-69.

9274

32.

4749

3417

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17.0

653

2.51

520.

948

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030

-0.0

83-0

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0-0

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020

lm01

21l2

0722

73.0

5065

-69.

3250

82.

4766

6616

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16.4

186

4.68

420.

998

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23-0

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0-0

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0-0

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00.

0020

lm03

21m

1701

8*80

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02-6

6.35

411

2.48

037

16.1

815

.84

1955

.670

20.

929

0.00

10-0

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0.00

20-0

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070

lm03

17k7

278

78.4

5743

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3560

12.

4809

6415

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15.1

342

0.77

690.

975

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060

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31-0

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0-0

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0.00

10lm

0344

k246

3682

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64-6

7.12

202

2.48

3249

15.5

215

.32

1091

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80.

961

-0.0

23-0

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-0.0

020

-0.0

040

0.00

20lm

0284

n199

5172

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19-6

7.24

532

2.48

3961

16.0

715

.80

1546

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40.

961

-0.0

050

-0.0

65-0

.007

0-0

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0.00

50lm

0167

l115

90*

74.2

5992

-68.

9369

72.

4847

1216

.77

16.5

843

4.72

450.

967

0.00

20-0

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0.00

10-0

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0.0

lm01

06k1

4838

76.2

3628

-70.

1988

22.

4853

3315

.62

15.5

522

50.5

739

0.93

5-0

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0-0

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-0.0

040

-0.0

83-0

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0lm

0550

n149

0375

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79-7

0.70

212.

4871

3616

.15

15.8

812

43.5

615

0.99

9-0

.047

-0.0

040

-0.0

040

-0.0

090

0.00

30lm

0427

l101

1075

.282

92-6

6.13

402

2.48

9254

16.7

216

.48

1927

.650

60.

944

-0.0

14-0

.073

-0.0

080

-0.0

430.

0lm

0331

k101

9881

.901

25-6

6.31

168

2.49

0214

16.5

116

.33

1455

.773

10.

983

-0.0

21-0

.02

-0.0

010

0.00

100.

0020

lm00

10l1

7439

*79

.983

71-6

9.32

095

2.49

3082

15.7

315

.50

1396

.903

60.

97-0

.006

0-0

.019

-0.0

030

-0.0

040

0.00

30lm

0307

k137

1576

.504

85-6

7.39

192.

4950

7416

.66

16.4

684

5.73

510.

979

-0.0

49-0

.06

-0.0

14-0

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-0.0

010

lm05

42l1

7356

72.9

7089

-71.

0678

82.

4955

6416

.59

16.5

418

11.7

353

0.98

7-0

.016

-0.0

120.

0020

-0.0

010

-0.0

lm04

57n6

420

80.8

3767

-66.

0913

52.

4956

5415

.64

15.4

119

51.7

180

0.89

7-0

.046

-0.1

18-0

.016

-0.0

450.

012

lm05

72k3

238*

79.5

0726

-70.

8194

72.

4959

6417

.66

17.5

811

26.6

354

0.94

60.

0070

-0.0

860.

0050

-0.0

41-0

.006

0lm

0040

k115

51*

86.0

9652

-69.

1266

12.

4992

3216

.99

16.7

816

34.5

805

0.97

1-0

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.031

0.0

-0.0

18-0

.001

0lm

0032

l206

4384

.010

87-6

9.69

192

2.49

9392

15.4

515

.24

1148

.593

00.

984

-0.0

070

-0.0

16-0

.0-0

.008

00.

0020

lm01

21l8

367*

73.1

5498

-69.

2507

42.

5007

7716

.28

16.0

713

06.4

884

0.97

3-0

.034

-0.0

3-0

.02

-0.0

170.

0020

lm00

15m

1964

381

.652

13-6

9.85

72.

5036

216

.82

16.6

638

7.75

720.

981

0.00

30-0

.04

-0.0

050

-0.0

31-0

.0lm

0045

k197

0686

.984

8-6

9.86

957

2.50

5617

15.0

514

.88

1589

.731

70.

988

-0.0

27-0

.024

-0.0

1-0

.017

-0.0

030

lm00

10m

6843

80.3

1027

-69.

0945

12.

5059

7415

.92

15.5

743

8.78

440.

946

0.00

20-0

.095

-0.0

1-0

.061

0.00

80lm

0303

m21

604

76.8

608

-66.

7263

92.

5070

116

.29

16.0

511

91.6

543

0.98

-0.0

35-0

.037

-0.0

010

-0.0

010

0.00

20lm

0346

m16

504

82.9

9672

-67.

4137

92.

5088

4115

.91

15.7

122

34.8

536

0.98

2-0

.001

0-0

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-0.0

020

-0.0

120.

0020

lm02

16l2

1415

82.6

6991

-69.

0143

42.

5094

0715

.99

15.8

121

90.7

652

0.98

5-0

.004

0-0

.037

0.00

10-0

.021

0.0

lm00

21l3

2167

82.7

9402

-69.

3864

22.

5122

8816

.64

16.7

474

8.77

380.

96-0

.04

-0.0

67-0

.018

-0.0

3-0

.002

0lm

0540

n138

6973

.497

76-7

0.69

082.

5127

5716

.07

15.8

918

33.6

867

0.93

5-0

.0-0

.084

0.0

-0.0

28-0

.0lm

0256

m23

734*

90.2

1733

-68.

8866

32.

5135

7417

.77

17.5

320

30.5

829

0.96

6-0

.006

0-0

.047

0.00

10-0

.03

0.0

lm05

96l1

9261

83.4

3063

-71.

8128

52.

5153

9217

.38

17.1

716

17.6

885

0.93

9-0

.038

-0.0

49-0

.001

0-0

.006

00.

0040

lm00

20l2

6644

81.8

095

-69.

3834

52.

5168

9916

.72

16.5

620

25.5

258

0.89

7-0

.08

-0.1

44-0

.037

-0.0

70.

0030

lm01

80l6

512

77.0

2743

-67.

8409

52.

5169

0915

.79

15.5

411

72.8

434

0.93

-0.0

35-0

.092

-0.0

15-0

.04

0.00

50lm

0567

k688

178

.047

49-7

1.54

482

2.52

0574

17.2

517

.11

2343

.572

50.

958

-0.0

34-0

.04

0.0

-0.0

030

-0.0

050

lm00

40m

2731

886

.377

98-6

9.22

432.

5221

3315

.72

15.6

019

41.6

268

0.86

8-0

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-0.1

82-0

.033

-0.0

880.

0020

lm03

43l2

2832

83.5

9525

-66.

8956

12.

5271

9315

.04

14.8

318

93.7

021

0.91

7-0

.006

0-0

.102

-0.0

030

-0.0

250.

0010

lm01

86n5

534

77.2

4272

-68.

8952

62.

5294

9516

.16

16.0

447

7.73

260.

951

-0.0

49-0

.087

-0.0

25-0

.049

-0.0

090

178


0206

m28

489

81.0

3877

-68.

8739

62.

5317

9116

.81

16.7

214

35.7

606

0.95

6-0

.009

0-0

.052

-0.0

080

-0.0

360.

0070

lm00

97n1

5434

79.4

1568

-70.

3575

12.

5325

1816

.27

16.0

619

57.6

478

0.90

6-0

.007

0-0

.116

-0.0

040

-0.0

430.

0010

lm00

15m

1357

681

.383

94-6

9.82

752.

5341

1716

.77

16.7

213

67.8

727

0.94

6-0

.036

-0.0

67-0

.019

-0.0

32-0

.003

0lm

0023

k356

482

.852

58-6

9.42

447

2.53

6665

17.1

317

.07

507.

5296

0.97

80.

0070

-0.0

6-0

.001

0-0

.047

-0.0

020

lm01

90m

1123

9*78

.964

18-6

7.71

148

2.53

8094

17.2

717

.10

1766

.913

00.

944

0.00

90-0

.081

-0.0

020

-0.0

65-0

.002

0lm

0294

l112

1674

.077

55-6

7.18

053

2.54

6991

16.6

016

.40

2256

.584

40.

962

-0.0

050

-0.0

54-0

.018

-0.0

25-0

.009

0lm

0010

l421

079

.840

39-6

9.23

612

2.55

1967

17.0

016

.86

588.

5004

0.94

3-0

.072

-0.1

04-0

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-0.0

63-0

.007

0lm

0466

n153

4781

.479

-66.

1622

32.

5527

2216

.68

16.6

279

5.76

990.

978

-0.0

19-0

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-0.0

020

0.0

-0.0

020

lm02

12n1

8380

82.7

2618

-68.

2714

62.

5538

9317

.21

17.2

315

30.7

138

0.95

50.

01-0

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-0.0

030

-0.0

56-0

.012

lm03

47m

1466

084

.048

89-6

7.40

174

2.55

4528

16.3

616

.10

1364

.938

70.

959

-0.0

12-0

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-0.0

17-0

.032

-0.0

060

lm00

10k1

7235

80.1

8843

-69.

1671

42.

5561

1116

.21

15.9

419

59.6

465

0.94

3-0

.001

0-0

.057

-0.0

010

-0.0

170.

0010

lm03

33l2

4619

82.0

1793

-66.

9016

12.

5567

0615

.71

15.5

119

77.6

400

0.98

-0.0

12-0

.02

-0.0

040

-0.0

090

0.00

10lm

0105

m14

713*

77.4

7108

-69.

8322

22.

5589

116

.83

16.6

814

96.6

366

0.97

90.

0020

-0.0

29-0

.001

0-0

.011

0.0

lm05

81m

2151

982

.779

34-7

0.57

647

2.55

9421

17.1

016

.95

1901

.844

00.

949

-0.0

63-0

.076

-0.0

28-0

.05

-0.0

050

lm01

55n2

2259

72.6

2359

-68.

6391

42.

5601

0517

.14

17.0

215

23.6

658

0.94

7-0

.051

-0.0

84-0

.02

-0.0

4-0

.002

0lm

0457

k246

6780

.380

14-6

6.07

433

2.56

1858

16.5

116

.27

1786

.763

30.

98-0

.008

0-0

.03

-0.0

050

-0.0

16-0

.001

0lm

0211

l166

6283

.549

77-6

7.90

057

2.56

1989

16.7

616

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1089

.684

90.

933

-0.0

-0.1

010.

0-0

.067

-0.0

010

lm01

00m

1626

676

.620

51-6

9.15

496

2.56

5832

16.7

416

.46

2303

.632

30.

937

-0.0

34-0

.074

-0.0

080

-0.0

180.

0010

lm01

70m

4805

75.2

3106

-67.

6807

62.

5662

3216

.19

15.8

633

4.90

630.

909

-0.0

49-0

.108

-0.0

21-0

.045

-0.0

040

lm03

16k1

4599

77.2

4938

-67.

3973

72.

5697

2616

.79

16.6

315

89.6

733

0.88

7-0

.01

-0.1

53-0

.012

-0.0

760.

0010

lm03

07m

1549

177

.249

16-6

7.39

742

2.56

975

16.7

816

.58

1463

.695

30.

916

0.00

20-0

.151

-0.0

010

-0.0

8-0

.007

0lm

0292

n237

0874

.270

14-6

6.94

127

2.56

9894

16.0

815

.84

2389

.511

40.

954

-0.0

060

-0.0

84-0

.002

0-0

.058

0.0

lm05

86l1

3797

81.4

6549

-71.

7383

72.

5741

0816

.37

16.1

816

03.6

181

0.91

1-0

.057

-0.1

25-0

.025

-0.0

56-0

.003

0lm

0112

l185

7574

.151

31-6

9.66

844

2.57

4239

16.5

616

.36

1711

.909

40.

963

-0.0

15-0

.026

-0.0

020

0.00

20-0

.0lm

0177

k176

6775

.825

58-6

8.81

452

2.57

7507

16.5

116

.28

1096

.671

10.

915

-0.0

13-0

.129

-0.0

-0.0

740.

0050

lm00

20k2

4655

82.1

3845

-69.

2302

62.

5793

3415

.95

15.7

312

66.6

051

0.95

70.

0050

-0.0

840.

0010

-0.0

610.

0lm

0602

l611

885

.658

51-7

0.99

859

2.58

0945

15.6

115

.68

390.

7804

0.97

2-0

.01

-0.0

35-0

.001

0-0

.015

0.0

lm02

11m

5293

83.8

299

-67.

6695

52.

5861

315

.95

15.7

018

33.8

282

0.98

2-0

.013

-0.0

63-0

.004

0-0

.048

0.00

10lm

0054

m17

797

88.2

2564

-69.

8642

82.

5867

4516

.09

15.9

815

38.7

375

0.95

1-0

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-0.0

49-0

.004

0-0

.01

0.00

10lm

0343

l256

1383

.616

61-6

6.91

348

2.58

9002

15.6

815

.49

2579

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30.

964

-0.0

080

-0.0

59-0

.006

0-0

.04

-0.0

040

lm03

41n5

260

83.8

6604

-66.

4727

22.

5895

514

.90

14.6

140

5.85

220.

974

-0.0

15-0

.024

0.00

30-0

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0030

lm03

55n2

6448

85.9

0168

-67.

2726

52.

5928

3815

.07

14.7

611

20.7

651

0.93

90.

0040

-0.0

890.

0030

-0.0

480.

0lm

0331

k181

3481

.882

85-6

6.36

722

2.59

5648

16.6

916

.50

1620

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70.

991

-0.0

070

-0.0

2-0

.004

0-0

.014

-0.0

lm00

41k2

1578

87.0

6688

-69.

1802

2.59

5659

17.0

316

.89

812.

7853

0.96

5-0

.046

-0.0

44-0

.004

0-0

.009

0-0

.002

0lm

0012

m28

1480

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38-6

9.42

642.

5989

16.8

416

.59

1804

.821

90.

980.

0030

-0.0

480.

0030

-0.0

35-0

.001

0lm

0366

n144

2886

.802

8-6

7.55

567

2.60

1096

17.1

617

.02

1899

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20.

962

-0.0

28-0

.03

0.00

100.

0010

0.00

20lm

0427

m16

528

75.7

7647

-66.

0217

82.

6082

2616

.28

15.9

951

7.59

340.

967

-0.0

12-0

.056

-0.0

080

-0.0

370.

0020

lm03

40n5

836

83.1

235

-66.

4399

92.

6144

5915

.75

15.4

714

63.7

628

0.93

5-0

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0-0

.105

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080

-0.0

7-0

.001

0lm

0040

k234

7685

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-69.

2081

22.

6154

1815

.90

15.7

019

01.7

951

0.97

5-0

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53-0

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-0.0

320.

0050

lm01

16l1

9585

*74

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44-7

0.38

601

2.61

797

16.7

216

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1447

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80.

975

-0.0

010

-0.0

43-0

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0-0

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0.00

80lm

0212

m20

099*

82.8

7114

-68.

1566

12.

6211

2816

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16.8

623

43.5

959

0.96

8-0

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0-0

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010

-0.0

21-0

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0

179

lm03

03n1

6128

76.8

2415

-66.

8436

42.

6211

9617

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16.8

625

35.7

713

0.94

7-0

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-0.0

91-0

.011

-0.0

68-0

.009

0lm

0551

m73

4376

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48-7

0.49

136

2.62

2983

17.3

317

.03

1126

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20.

912

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72-0

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27-0

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010

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77l5

586

89.1

5001

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6027

32.

6288

9416

.59

16.3

118

61.7

884

0.93

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47-0

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15-0

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-0.0

010

lm00

20l9

813

81.9

2152

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2723

32.

6313

5215

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15.5

843

4.67

090.

942

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090

-0.0

87-0

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0-0

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020

lm03

45k1

3606

83.5

5195

-67.

0449

22.

6315

3414

.90

14.7

139

5.68

780.

929

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27-0

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11-0

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lm03

16l1

7312

77.6

4399

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5734

32.

6316

3116

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16.3

419

06.8

206

0.98

2-0

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0-0

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020

-0.0

17-0

.001

0lm

0183

l171

8577

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33-6

8.24

991

2.63

4221

17.1

017

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2517

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80.

981

-0.0

15-0

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060

-0.0

150.

0010

lm00

90n2

9324

78.3

4942

-69.

3802

2.63

6584

15.9

615

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2009

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50.

952

0.0

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19-0

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780.

011

lm05

43n1

8447

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33-7

1.05

282.

6377

616

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16.5

121

98.7

862

0.96

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030

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68-0

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0-0

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0.00

10lm

0220

n197

91*

84.8

0013

-67.

9317

22.

6411

8816

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16.5

123

05.7

351

0.97

2-0

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0-0

.038

-0.0

060

-0.0

280.

0010

lm03

35n2

4071

82.4

5012

-67.

2493

22.

6414

0316

.14

15.9

114

63.7

486

0.99

-0.0

090

-0.0

170.

0020

-0.0

-0.0

030

lm02

94l2

1960

73.9

8799

-67.

2495

82.

6414

2715

.39

15.1

715

75.6

394

0.96

3-0

.019

-0.0

31-0

.001

0-0

.002

00.

0040

lm02

00l6

405

80.5

8213

-67.

8414

62.

6490

4215

.77

15.5

823

29.6

599

0.98

7-0

.009

0-0

.022

-0.0

050

-0.0

140.

0010

lm01

30m

1478

0*70

.566

84-6

9.14

122.

6506

7417

.75

17.5

618

38.6

513

0.94

50.

0050

-0.0

6-0

.005

0-0

.041

0.00

50lm

0465

l267

3682

.048

34-6

5.88

179

2.65

4428

15.8

615

.63

1761

.832

30.

92-0

.034

-0.0

9-0

.01

-0.0

250.

0080

lm01

84k1

7447

76.9

537

-68.

4594

42.

6561

7316

.54

16.4

113

74.9

038

0.88

5-0

.088

-0.1

79-0

.043

-0.0

950.

0010

lm02

16l1

7243

82.5

3308

-68.

9827

82.

6573

9215

.88

15.7

414

24.8

947

0.92

4-0

.045

-0.1

06-0

.018

-0.0

360.

0010

lm00

13l2

1404

81.1

5178

-69.

6697

52.

6580

9716

.67

16.5

818

66.6

505

0.99

2-0

.019

-0.0

18-0

.0-0

.003

00.

0lm

0037

n105

99*

85.5

9315

-70.

3281

82.

6586

9816

.45

16.3

323

23.6

869

0.98

5-0

.003

0-0

.032

-0.0

020

-0.0

14-0

.0lm

0124

m15

092

72.4

8036

-69.

8495

72.

6591

2916

.47

16.3

822

31.5

516

0.96

8-0

.03

-0.0

36-0

.0-0

.0-0

.001

0lm

0173

m21

250*

76.5

2163

-68.

1156

32.

6613

3416

.02

15.7

111

39.7

472

0.97

6-0

.014

-0.0

49-0

.009

0-0

.039

0.0

lm02

30l9

562

86.3

1025

-67.

8684

52.

6626

5817

.05

16.8

917

75.9

264

0.89

6-0

.046

-0.1

38-0

.022

-0.0

590.

0020

lm01

73n1

3333

76.4

494

-68.

2276

2.66

5684

17.2

917

.14

1468

.607

81.

003

-0.0

14-0

.023

-0.0

050

-0.0

20.

0020

lm01

15k4

086

74.9

1607

-69.

7776

32.

6661

7715

.36

15.2

422

80.5

789

0.98

3-0

.025

-0.0

28-0

.002

00.

0-0

.004

0lm

0195

m16

673*

80.2

7267

-68.

4434

42.

6664

7616

.11

15.9

111

36.8

411

0.96

3-0

.004

0-0

.047

-0.0

040

-0.0

190.

0020

lm01

55m

2848

372

.700

91-6

8.52

691

2.66

7227

16.8

416

.58

1833

.661

00.

976

0.00

60-0

.044

-0.0

020

-0.0

29-0

.002

0lm

0344

m24

630

83.2

5301

-67.

1157

22.

6678

9615

.46

15.2

312

56.5

883

0.98

5-0

.006

0-0

.028

-0.0

050

-0.0

20.

0lm

0127

l964

273

.143

06-7

0.31

871

2.66

9394

16.8

816

.63

2471

.865

20.

975

-0.0

38-0

.035

-0.0

18-0

.033

0.00

10lm

0285

m10

287

73.3

7918

-67.

0160

82.

6697

2515

.30

15.1

221

99.7

855

0.96

-0.0

040

-0.0

39-0

.006

0-0

.015

0.00

40lm

0045

k104

45*

87.1

6535

-69.

8126

2.66

9896

15.7

815

.66

2269

.745

60.

950.

0-0

.086

0.00

10-0

.063

0.0

lm00

11m

2271

381

.372

01-6

9.18

227

2.67

4348

16.1

315

.86

1711

.936

20.

980.

0030

-0.0

34-0

.003

0-0

.019

0.00

10lm

0125

m55

8973

.748

55-6

9.77

929

2.67

6261

15.0

414

.77

1076

.695

00.

957

-0.0

010

-0.0

69-0

.002

0-0

.036

-0.0

010

lm01

74l1

2903

*74

.826

39-6

8.60

046

2.67

6506

17.5

317

.43

1848

.631

80.

920.

0010

-0.0

45-0

.002

0-0

.015

0.00

40lm

0330

n193

00*

81.3

2542

-66.

5302

32.

6772

6217

.72

17.7

619

68.6

406

0.97

60.

0030

-0.0

48-0

.005

0-0

.035

0.00

20lm

0685

n231

9177

.555

07-7

2.85

828

2.67

8273

17.2

517

.13

2214

.778

90.

926

-0.0

-0.1

2-0

.001

0-0

.068

-0.0

020

lm01

86n8

773

77.3

7151

-68.

9172

42.

6788

3215

.08

14.8

149

6.67

190.

947

-0.0

25-0

.076

-0.0

15-0

.051

0.00

60lm

0022

k389

0*82

.138

9-6

9.43

238

2.68

0612

16.5

716

.48

1941

.620

20.

98-0

.0-0

.036

-0.0

010

-0.0

230.

0020

lm00

92m

3797

*78

.430

77-6

9.43

449

2.68

3288

17.3

617

.31

1096

.687

70.

97-0

.004

0-0

.062

-0.0

010

-0.0

39-0

.004

0lm

0093

m11

981

79.4

2347

-69.

4660

62.

6873

716

.31

16.1

717

71.8

776

0.93

2-0

.046

-0.0

82-0

.019

-0.0

420.

0040

lm05

71n2

6162

80.6

4243

-70.

752.

6874

316

.07

15.8

435

1.81

870.

972

-0.0

080

-0.0

4-0

.006

0-0

.023

-0.0

lm01

77l2

1797

75.9

4157

-69.

0056

12.

6874

8916

.96

16.7

323

07.6

238

0.98

3-0

.025

-0.0

380.

0020

-0.0

010

-0.0

030

180


0530

m21

215

71.5

4592

-70.

5860

82.

6876

3816

.26

16.0

223

05.6

051

0.95

4-0

.026

-0.0

71-0

.007

0-0

.015

-0.0

010

lm01

65k2

8784

73.9

2743

-68.

5188

52.

6917

5416

.85

16.8

311

07.8

097

0.88

7-0

.05

-0.1

6-0

.036

-0.0

820.

014

lm05

64k4

754

77.1

4207

-71.

1755

42.

6928

8816

.11

15.9

510

70.8

255

0.98

3-0

.004

0-0

.023

-0.0

040

-0.0

140.

0010

lm02

41k1

3248

*88

.963

94-6

7.74

821

2.69

5078

16.9

316

.73

2143

.826

10.

945

-0.0

010

-0.0

67-0

.002

0-0

.022

0.00

30lm

0165

k136

1274

.304

69-6

8.43

168

2.69

6423

15.1

414

.93

1928

.575

70.

967

-0.0

060

-0.0

5-0

.003

0-0

.034

-0.0

030

lm02

13k2

3159

*83

.448

48-6

8.13

261

2.70

0634

16.9

416

.82

1906

.844

80.

984

-0.0

030

-0.0

34-0

.006

0-0

.013

-0.0

060

lm02

15m

2414

83.6

6528

-68.

3654

62.

7016

1216

.01

15.7

914

83.6

936

0.97

1-0

.01

-0.0

11-0

.055

-0.0

170.

023

lm02

91l5

438

74.8

6958

-66.

4304

72.

7036

815

.88

15.7

418

09.7

745

0.90

9-0

.048

-0.1

37-0

.02

-0.0

550.

0020

lm02

13n3

0527

*83

.703

61-6

8.32

958

2.70

3828

17.1

517

.03

858.

6189

0.95

2-0

.003

0-0

.091

-0.0

060

-0.0

850.

0020

lm01

15k1

7125

75.0

8609

-69.

8496

32.

7078

4216

.52

16.4

311

54.8

513

0.89

1-0

.061

-0.1

4-0

.028

-0.0

60.

0060

lm01

64m

2684

473

.458

52-6

8.50

987

2.70

9069

17.2

317

.16

1898

.736

90.

959

-0.0

16-0

.062

-0.0

25-0

.032

0.01

3lm

0015

m15

054

81.7

0531

-69.

8325

52.

7098

7217

.03

16.9

912

24.5

329

0.96

9-0

.002

0-0

.025

-0.0

1-0

.007

00.

0070

lm00

12n1

4828

80.4

5366

-69.

6430

72.

7128

716

.09

15.9

318

78.6

691

0.97

1-0

.026

-0.0

42-0

.01

-0.0

22-0

.002

0lm

0103

k105

8276

.958

48-6

9.46

051

2.71

3007

16.0

916

.03

414.

7172

0.91

4-0

.055

-0.1

11-0

.025

-0.0

470.

0060

lm04

31n1

5433

77.3

05-6

5.17

407

2.71

4038

16.9

316

.76

2096

.874

30.

932

-0.0

53-0

.064

-0.0

11-0

.021

0.00

90lm

0311

n213

5278

.704

5-6

6.54

172.

7150

9716

.44

16.2

614

63.7

082

0.93

2-0

.059

-0.1

04-0

.026

-0.0

530.

0010

lm01

85n2

2544

*78

.190

87-6

8.69

732.

7182

17.3

517

.22

1851

.612

00.

963

-0.0

15-0

.064

-0.0

17-0

.051

-0.0

010

lm03

33m

2212

0*82

.202

73-6

6.73

199

2.72

0332

15.9

215

.66

1184

.674

80.

978

-0.0

070

-0.0

31-0

.002

0-0

.009

00.

0020

lm03

25k2

8914

*80

.037

64-6

7.12

965

2.72

169

16.6

316

.52

1493

.710

20.

932

-0.0

090

-0.0

63-0

.004

0-0

.004

00.

0010

lm01

72n6

253

75.2

7408

-68.

1923

52.

7276

6315

.53

15.2

977

5.85

990.

956

-0.0

16-0

.075

-0.0

050

-0.0

520.

0010

lm02

06k2

5944

80.8

1531

-68.

8697

42.

7314

616

.21

16.0

317

30.9

271

0.98

1-0

.027

-0.0

35-0

.001

0-0

.003

00.

0030

lm02

94l8

864

73.7

6054

-67.

1642

52.

7403

8815

.14

14.7

712

53.5

437

0.94

5-0

.009

0-0

.087

-0.0

060

-0.0

630.

0lm

0091

m28

603*

79.7

0007

-69.

2096

62.

7408

916

.96

16.8

111

93.6

169

0.95

20.

0020

-0.0

53-0

.002

0-0

.029

-0.0

030

lm01

23k1

7044

73.2

29-6

9.49

675

2.74

4816

15.5

215

.42

1581

.589

60.

963

-0.0

19-0

.033

0.00

100.

0020

0.00

30lm

0027

l194

2083

.109

67-7

0.38

774

2.74

5088

16.8

916

.82

1435

.763

80.

931

-0.0

61-0

.085

-0.0

18-0

.038

0.01

3lm

0020

k168

2681

.949

32-6

9.17

409

2.74

7223

15.3

515

.17

569.

5124

0.91

7-0

.043

-0.1

11-0

.022

-0.0

490.

0030

lm02

05m

4021

81.9

9126

-68.

3726

82.

7498

6617

.02

16.8

510

82.8

700

1.00

7-0

.027

-0.0

15-0

.007

0-0

.009

0-0

.003

0lm

0294

n747

974

.528

13-6

7.15

228

2.75

026

16.1

915

.97

2192

.686

50.

962

-0.0

26-0

.036

0.00

200.

00.

0030

lm02

04l1

8900

80.5

3603

-68.

6208

52.

7545

0317

.23

17.0

521

98.6

817

0.91

80.

0070

-0.0

840.

0090

-0.0

55-0

.009

0lm

0231

l120

15*

87.0

4159

-67.

8789

32.

7548

2416

.67

16.4

918

79.6

968

0.99

20.

0050

-0.0

250.

0020

-0.0

21-0

.001

0lm

0036

m17

521

84.4

2606

-70.

2157

52.

7558

5616

.42

16.2

649

1.59

810.

956

-0.0

15-0

.067

-0.0

070

-0.0

410.

0040

lm05

56n1

7386

*75

.721

5-7

1.79

254

2.75

5996

17.8

517

.67

2200

.767

50.

968

-0.0

11-0

.045

-0.0

060

-0.0

330.

0070

lm04

17n1

7063

74.2

1734

-66.

1814

92.

7602

8816

.55

16.3

918

20.6

634

0.96

-0.0

010

-0.0

5-0

.001

0-0

.026

0.00

10lm

0091

n214

5279

.642

53-6

9.39

339

2.76

5244

16.9

516

.84

2161

.754

30.

947

-0.0

77-0

.093

-0.0

28-0

.06

-0.0

040

lm06

11m

4959

89.1

808

-70.

4687

72.

7675

1416

.87

16.6

122

37.6

572

0.93

6-0

.004

0-0

.115

-0.0

020

-0.0

79-0

.002

0lm

0541

k200

99*

73.7

4083

-70.

5796

52.

7681

5617

.12

17.0

222

58.7

505

0.97

2-0

.008

0-0

.05

-0.0

030

-0.0

17-0

.002

0lm

0093

l260

3079

.190

29-6

9.69

22.

7722

5716

.76

16.7

723

49.5

849

0.97

5-0

.03

-0.0

23-0

.002

0-0

.002

0-0

.004

0lm

0025

k174

8982

.895

83-6

9.85

245

2.77

3556

16.9

516

.90

1480

.846

30.

937

-0.0

070

-0.0

94-0

.001

0-0

.046

-0.0

020

lm01

76k2

5619

75.0

7291

-68.

8768

42.

7744

8915

.73

15.5

018

84.6

086

0.92

5-0

.027

-0.0

77-0

.008

0-0

.015

0.01

1lm

0346

n230

0383

.175

1-6

7.62

429

2.77

7051

15.2

914

.97

1258

.592

60.

942

-0.0

010

-0.0

88-0

.005

0-0

.052

-0.0

020

lm01

77n1

0023

76.2

5629

-68.

9224

52.

7777

7516

.35

16.2

036

1.86

580.

962

-0.0

37-0

.053

-0.0

12-0

.022

-0.0

020

181

lm00

33k1

1425

84.8

4785

-69.

4691

52.

7808

3515

.79

15.7

336

5.75

260.

951

-0.0

2-0

.039

0.00

100.

0020

0.00

70lm

0604

l252

6885

.558

37-7

1.47

772

2.78

1504

16.2

916

.13

1819

.813

80.

955

-0.0

16-0

.03

0.00

30-0

.001

0-0

.0lm

0427

k156

8575

.526

56-6

6.07

629

2.79

1595

15.8

315

.53

1946

.681

50.

963

-0.0

22-0

.038

0.0

0.00

100.

0040

lm03

37k1

8241

81.9

6413

-67.

4289

52.

7939

9515

.50

15.3

122

07.6

279

0.98

80.

0040

-0.0

27-0

.001

0-0

.019

-0.0

030

lm05

80m

1660

4*81

.833

25-7

0.55

214

2.79

6134

16.6

816

.51

1894

.742

30.

964

-0.0

020

-0.0

46-0

.001

0-0

.036

0.00

20lm

0156

m24

0171

.936

-68.

7904

62.

7971

7216

.26

16.1

318

30.6

572

0.96

9-0

.02

-0.0

310.

0010

0.0

-0.0

010

lm03

44m

1620

0*83

.147

81-6

7.06

121

2.79

8582

16.2

616

.06

1820

.720

20.

984

-0.0

060

-0.0

3-0

.004

0-0

.023

-0.0

010

lm02

94l8

466

73.9

4168

-67.

1618

12.

8016

5816

.87

16.6

783

5.61

820.

991

-0.0

13-0

.022

-0.0

13-0

.011

0.00

10lm

0343

k468

383

.411

75-6

6.62

775

2.80

5072

15.2

515

.01

2580

.728

40.

91-0

.041

-0.1

3-0

.016

-0.0

610.

0060

lm01

62m

2487

8*73

.484

37-6

8.17

82.

8088

4816

.31

16.2

822

94.6

311

0.94

60.

0010

-0.0

74-0

.003

0-0

.029

0.00

10lm

0466

l164

61*

81.3

4921

-66.

2344

72.

8151

615

.73

15.7

020

21.5

871

0.97

3-0

.004

0-0

.021

-0.0

030

-0.0

030

0.00

10lm

0214

n174

17*

82.9

1098

-68.

6131

42.

8161

0817

.67

17.6

018

39.7

094

0.97

1-0

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-0.0

34-0

.004

0-0

.021

-0.0

040

lm03

36k7

065

80.8

5757

-67.

3433

12.

8212

5816

.06

15.9

614

47.8

177

0.95

7-0

.02

-0.0

40.

0010

0.00

100.

0050

lm01

91n4

635

80.2

1988

-67.

8643

52.

8226

1117

.01

16.8

820

31.5

042

0.90

8-0

.08

-0.1

43-0

.033

-0.0

66-0

.004

0lm

0351

n102

67*

85.7

2673

-66.

5861

12.

8255

601

17.1

317

.00

1189

.710

00.

977

-0.0

050

-0.0

23-0

.001

0-0

.004

00.

0010

lm01

06l1

1713

75.9

1194

-70.

3326

22.

8275

0115

.85

15.6

217

55.8

780

0.96

2-0

.011

-0.0

61-0

.008

0-0

.047

-0.0

lm00

14m

9900

*80

.389

68-6

9.81

157

2.83

114

17.6

217

.60

1442

.808

10.

971

-0.0

070

-0.0

45-0

.003

0-0

.041

-0.0

050

lm02

04k9

178*

80.6

2568

-68.

4060

52.

8392

7816

.25

16.2

119

27.7

495

0.96

50.

0-0

.038

-0.0

020

-0.0

070

0.00

10lm

0032

k156

6084

.044

61-6

9.53

401

2.84

1496

14.7

214

.52

1449

.782

20.

965

-0.0

050

-0.0

59-0

.004

0-0

.038

-0.0

1lm

0195

n547

279

.951

77-6

8.53

449

2.84

1972

16.8

716

.85

759.

8540

0.89

2-0

.083

-0.1

49-0

.039

-0.0

84-0

.005

0lm

0581

l290

1082

.620

01-7

0.76

699

2.84

3662

16.7

316

.71

2008

.560

10.

943

-0.0

5-0

.081

-0.0

2-0

.032

0.00

50lm

0020

n128

40*

82.3

8831

-69.

2866

72.

8512

7616

.98

16.7

323

45.5

803

0.95

4-0

.009

0-0

.053

-0.0

070

-0.0

140.

0030

lm00

34k1

2920

*84

.066

26-6

9.83

668

2.85

2214

116

.30

16.1

719

97.5

843

0.92

8-0

.005

0-0

.095

0.00

30-0

.035

0.00

20lm

0021

k137

7082

.917

11-6

9.13

302

2.85

3292

15.3

315

.09

797.

5801

0.88

-0.0

68-0

.171

-0.0

31-0

.086

0.00

10lm

0541

m10

971

74.4

8554

-70.

5098

22.

8619

3416

.96

16.7

721

88.6

643

0.95

2-0

.052

-0.0

68-0

.013

-0.0

290.

0010

lm00

31k1

9705

85.2

061

-69.

2183

62.

8675

3614

.91

14.9

719

77.6

787

0.91

6-0

.02

-0.0

86-0

.006

0-0

.024

0.00

30lm

0011

n104

45*

81.2

678

-69.

2638

2.86

7908

16.1

616

.07

727.

8740

0.97

-0.0

040

-0.0

36-0

.004

0-0

.013

0.0

lm04

24n2

3353

75.0

9632

-65.

8668

92.

8693

1215

.03

14.6

833

2.84

290.

948

-0.0

070

-0.0

85-0

.005

0-0

.051

0.00

20lm

0314

m22

740

77.7

2598

-67.

0924

2.87

1881

16.7

716

.81

1128

.683

80.

89-0

.076

-0.1

49-0

.038

-0.0

660.

0040

lm01

65k1

9767

*74

.304

45-6

8.46

583

2.87

351

16.9

916

.92

1407

.911

70.

97-0

.016

-0.0

51-0

.011

-0.0

47-0

.001

0lm

0321

k150

88*

80.2

1354

-66.

4235

32.

8764

5617

.00

16.8

311

22.6

202

0.99

5-0

.003

0-0

.016

-0.0

010

-0.0

060

0.00

10lm

0013

k297

8881

.088

15-6

9.56

005

2.88

2388

15.9

315

.95

2329

.656

70.

974

-0.0

29-0

.028

0.00

30-0

.002

00.

0010

lm00

31l2

1280

85.0

1322

-69.

3319

22.

8824

8916

.08

15.9

922

57.6

709

0.97

9-0

.002

0-0

.023

-0.0

11-0

.011

0.00

50lm

0285

m24

289

73.5

7847

-67.

1068

32.

8833

6116

.38

16.1

518

38.6

761

0.97

7-0

.002

0-0

.032

-0.0

040

-0.0

170.

0lm

0417

m19

623

74.2

255

-66.

0741

62.

8855

215

.85

15.5

718

86.5

721

0.95

7-0

.029

-0.0

47-0

.005

0-0

.008

00.

0040

lm01

05k3

1240

77.0

4771

-69.

9283

82.

8878

5417

.14

17.0

615

03.6

434

0.93

9-0

.042

-0.0

620.

0010

-0.0

040

0.00

90lm

0541

l179

0673

.856

15-7

0.78

171

2.89

5575

16.8

116

.74

1835

.688

30.

921

-0.0

69-0

.129

-0.0

31-0

.07

-0.0

010

lm03

31m

1772

382

.189

19-6

6.36

106

2.89

6212

16.9

216

.65

792.

7472

0.97

6-0

.004

0-0

.03

-0.0

070

-0.0

18-0

.001

0lm

0110

l205

2574

.090

64-6

9.34

248

2.89

896

16.4

616

.28

1881

.608

60.

950.

0060

-0.0

94-0

.002

0-0

.065

0.00

90lm

0103

k151

9877

.065

-69.

4846

2.89

9283

15.8

015

.96

2270

.737

10.

973

-0.0

-0.0

4-0

.0-0

.034

0.00

10lm

0364

k699

786

.162

38-6

7.00

003

2.90

0784

17.0

216

.87

456.

7497

0.95

80.

0010

-0.0

590.

0020

-0.0

290.

0010

182


0166

l185

1173

.077

86-6

8.98

609

2.90

2615

.65

15.4

242

6.73

820.

962

-0.0

24-0

.036

0.00

300.

00.

0040

lm01

20n2

4579

*72

.503

89-6

9.35

576

2.90

7138

15.8

715

.82

1083

.817

50.

976

-0.0

070

-0.0

29-0

.004

0-0

.005

0-0

.0lm

0345

k233

1083

.835

1-6

7.10

524

2.90

8255

15.8

915

.65

1994

.588

80.

966

-0.0

030

-0.0

46-0

.027

-0.0

080

0.01

5lm

0327

m59

2780

.558

27-6

7.33

953

2.91

1755

15.8

815

.61

1290

.519

60.

918

-0.0

030

-0.1

38-0

.002

0-0

.081

-0.0

010

lm02

85n6

767

73.5

462

-67.

1495

42.

9117

617

.23

17.0

019

22.6

488

0.97

8-0

.011

-0.0

45-0

.006

0-0

.038

0.00

20lm

0701

l689

2*81

.739

71-7

2.03

963

2.91

2402

17.0

216

.89

1528

.672

00.

968

-0.0

040

-0.0

38-0

.004

0-0

.008

00.

0010

lm02

16n1

5995

83.1

3799

-68.

9625

62.

9135

1414

.86

14.7

420

56.4

677

0.87

5-0

.056

-0.1

76-0

.024

-0.0

750.

0lm

0614

l199

70*

87.5

7282

-71.

4431

92.

9165

2217

.16

17.3

422

04.8

174

0.95

8-0

.002

0-0

.046

0.00

20-0

.027

-0.0

030

lm03

23n7

828

80.3

9908

-66.

7974

22.

9168

0116

.43

16.2

440

5.80

070.

945

-0.0

030

-0.0

84-0

.001

0-0

.042

-0.0

020

lm00

24m

7552

82.6

9505

-69.

8000

12.

9172

0816

.12

16.0

014

80.8

463

0.88

7-0

.084

-0.1

59-0

.039

-0.0

790.

012

lm01

20m

1197

372

.670

68-6

9.12

053

2.91

7753

15.9

215

.72

1766

.881

50.

919

-0.0

46-0

.104

-0.0

14-0

.042

0.01

lm00

25k3

1765

82.9

931

-69.

9255

82.

9180

3916

.62

16.5

614

80.8

463

0.94

90.

0020

-0.0

8-0

.009

0-0

.05

-0.0

080

lm03

00k8

884

75.7

5457

-66.

3069

62.

9218

3416

.91

16.6

414

63.6

953

0.96

9-0

.009

0-0

.054

-0.0

020

-0.0

420.

0050

lm02

94m

2862

374

.274

29-6

7.12

564

2.92

2208

16.1

215

.98

1472

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60.

978

-0.0

010

-0.0

440.

0040

-0.0

280.

0lm

0426

n179

4975

.105

64-6

6.17

679

2.92

4628

16.4

716

.18

2187

.695

80.

982

-0.0

1-0

.024

-0.0

060

-0.0

120.

0020

lm02

96m

2340

674

.180

81-6

7.45

372.

9249

4216

.77

16.5

984

5.72

830.

979

-0.0

11-0

.032

-0.0

080

-0.0

230.

0010

lm03

03m

5318

76.9

2088

-66.

6270

42.

9260

8217

.10

16.9

381

9.79

950.

957

-0.0

030

-0.0

730.

0-0

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-0.0

010

lm00

21k2

4967

83.2

0222

-69.

2013

22.

9261

15.4

315

.19

1259

.600

70.

945

0.00

60-0

.082

0.00

10-0

.051

-0.0

010

lm01

10l2

1211

*73

.918

3-6

9.34

737

2.92

6536

16.8

916

.70

1771

.864

90.

961

-0.0

080

-0.0

69-0

.011

-0.0

540.

0010

lm03

35l8

729

81.8

3248

-67.

1595

82.

9316

1816

.39

16.2

780

9.68

470.

909

-0.0

11-0

.123

-0.0

050

-0.0

420.

0lm

0560

m74

9377

.458

08-7

0.49

391

2.93

4794

16.1

116

.17

1140

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50.

954

-0.0

43-0

.061

-0.0

12-0

.032

0.00

40lm

0312

n157

41*

77.9

4811

-66.

8564

2.93

5118

16.8

616

.55

2131

.805

70.

979

-0.0

080

-0.0

28-0

.004

0-0

.015

-0.0

020

lm01

12n2

1013

74.4

5324

-69.

6794

72.

9385

6115

.11

14.9

323

15.6

271

0.97

6-0

.013

-0.0

29-0

.002

0-0

.007

00.

0020

lm03

40k2

2602

*82

.881

6-6

6.42

372

2.94

0286

17.7

217

.52

1941

.775

00.

968

0.00

10-0

.057

-0.0

010

-0.0

170.

0010

lm00

41n7

760*

87.2

648

-69.

2617

32.

9454

0217

.39

17.3

612

72.6

320

0.96

9-0

.01

-0.0

39-0

.004

0-0

.011

0.00

10lm

0326

l110

0379

.359

85-6

7.52

361

2.94

932

17.2

217

.02

1855

.787

50.

962

-0.0

080

-0.0

55-0

.009

0-0

.027

-0.0

1lm

0051

n154

6889

.468

55-6

9.30

452

2.94

9872

17.0

516

.86

1883

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90.

952

-0.0

36-0

.049

-0.0

-0.0

060

0.00

30lm

0344

k132

9782

.770

59-6

7.04

496

2.95

0326

15.6

515

.44

2265

.805

00.

985

0.00

40-0

.015

-0.0

030

-0.0

050

-0.0

010

lm01

14k2

6929

74.0

5413

-69.

9213

12.

9509

0315

.96

15.8

011

37.8

006

0.96

6-0

.001

0-0

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-0.0

060

-0.0

22-0

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0lm

0230

l976

7*86

.119

41-6

7.86

997

2.95

3796

17.2

817

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384.

8400

0.96

2-0

.008

0-0

.054

-0.0

060

-0.0

43-0

.0lm

0207

m16

357

82.0

992

-68.

8051

22.

9565

6715

.30

15.0

417

59.8

484

0.90

8-0

.011

-0.1

31-0

.006

0-0

.076

-0.0

020

lm01

01k2

4223

*76

.998

18-6

9.20

342.

9590

616

.39

16.3

019

05.7

517

0.91

3-0

.01

-0.1

16-0

.001

0-0

.05

0.0

lm01

22m

2614

*72

.711

73-6

9.41

842

2.96

3894

16.0

415

.83

2172

.692

20.

969

0.00

40-0

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-0.0

010

-0.0

280.

0lm

0112

k210

2474

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42-6

9.55

692.

9663

0715

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15.2

642

8.62

440.

985

-0.0

19-0

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010

0.00

10-0

.001

0lm

0347

m23

821

83.9

5327

-67.

4656

92.

9709

9415

.77

15.5

211

90.7

742

0.98

-0.0

1-0

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-0.0

080

-0.0

130.

0lm

0032

n105

7084

.625

91-6

9.62

399

2.97

1654

15.7

315

.57

403.

6255

0.98

8-0

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-0.0

18-0

.001

0-0

.002

0-0

.002

0lm

0090

k350

478

.103

37-6

9.07

876

2.97

2621

15.7

315

.61

380.

7049

0.98

4-0

.012

-0.0

44-0

.006

0-0

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0.00

10lm

0335

k267

5682

.003

23-6

7.11

539

2.97

543

16.3

616

.32

1964

.640

80.

895

-0.0

79-0

.168

-0.0

45-0

.085

-0.0

1lm

0444

n156

0778

.124

41-6

5.80

446

2.97

7039

17.0

316

.94

1793

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00.

948

-0.0

26-0

.037

0.00

300.

0020

0.00

10lm

0294

m48

2574

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03-6

6.98

277

2.97

779

15.1

814

.95

1306

.495

00.

959

-0.0

3-0

.058

-0.0

090

-0.0

20.

0010

lm03

31k2

3717

*81

.790

68-6

6.42

442

2.99

0145

416

.42

16.3

016

60.5

094

0.96

1-0

.014

-0.0

350.

0030

-0.0

010

0.00

80

183

lm00

93m

1791

4*79

.462

77-6

9.49

655

3.01

1134

116

.08

15.9

636

1.78

240.

886

-0.0

75-0

.159

-0.0

44-0

.083

0.00

60lm

0224

m10

741*

84.8

0999

-68.

4181

43.

0232

527

16.3

316

.23

1059

.921

70.

926

0.00

10-0

.083

0.0

-0.0

17-0

.0lm

0017

m23

847

81.5

1398

-70.

2537

13.

0245

3517

.02

16.8

951

1.53

740.

992

0.0

-0.0

36-0

.003

0-0

.018

-0.0

010

lm00

33k1

7847

*85

.064

8-6

9.50

791

3.02

5998

115

.54

15.4

219

97.5

843

0.97

6-0

.007

0-0

.042

-0.0

080

-0.0

250.

0040

lm05

41n1

5871

74.3

8819

-70.

7380

53.

0272

116

.46

16.2

510

77.7

004

0.98

3-0

.003

0-0

.016

-0.0

020

-0.0

060

-0.0

020

lm00

21n5

306

83.4

1862

-69.

2315

33.

0399

1614

.86

14.7

120

07.5

547

0.98

8-0

.01

-0.0

2-0

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.001

00.

0010

lm01

33n1

1237

*71

.466

63-6

9.61

311

3.04

2348

17.0

516

.94

1478

.573

90.

948

-0.0

020

-0.0

74-0

.001

0-0

.037

-0.0

1lm

0551

m22

887

76.6

378

-70.

5936

23.

0449

2915

.41

15.0

910

94.7

740

0.93

5-0

.034

-0.0

89-0

.012

-0.0

260.

0020

lm03

13m

1266

6*78

.796

19-6

6.67

068

3.04

777

17.4

817

.32

2298

.685

60.

938

0.00

50-0

.102

-0.0

070

-0.0

75-0

.004

0lm

0191

n374

380

.036

16-6

7.85

401

3.05

3936

16.3

716

.27

1162

.681

70.

942

-0.0

16-0

.056

-0.0

010

-0.0

020

0.00

40lm

0333

k294

7481

.859

84-6

6.77

636

3.05

7151

15.5

115

.33

1961

.749

30.

97-0

.015

-0.0

290.

0010

-0.0

010

0.00

40lm

0426

n226

20*

75.0

737

-66.

2125

53.

0586

2616

.37

16.0

815

93.6

165

0.98

3-0

.008

0-0

.028

-0.0

060

-0.0

160.

0010

lm03

30m

5632

81.4

9411

-66.

2831

3.06

1442

15.6

415

.36

1277

.543

70.

978

-0.0

090

-0.0

36-0

.015

-0.0

270.

0lm

0045

k150

0786

.914

72-6

9.84

105

3.06

3892

16.6

416

.78

327.

8286

0.91

4-0

.065

-0.1

3-0

.025

-0.0

710.

0080

lm00

33l2

4296

85.1

0421

-69.

6997

43.

0665

0915

.45

15.4

315

79.7

131

0.90

9-0

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-0.0

81-0

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.006

00.

016

lm01

05l1

3533

77.0

2341

-70.

0387

73.

0665

3616

.06

15.8

818

54.6

134

0.97

6-0

.019

-0.0

260.

0020

-0.0

020

0.00

30lm

0022

n144

8082

.567

15-6

9.64

186

3.06

8277

16.1

115

.95

2516

.865

20.

982

-0.0

040

-0.0

35-0

.005

0-0

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-0.0

030

lm05

64k2

0997

77.4

4903

-71.

2801

63.

0742

1915

.10

14.8

915

72.7

651

0.98

2-0

.005

0-0

.023

-0.0

020

-0.0

020

0.00

10lm

0020

k189

27*

82.0

6909

-69.

1891

83.

0817

6415

.73

15.5

687

8.60

140.

937

-0.0

040

-0.0

76-0

.001

0-0

.017

-0.0

lm05

47l6

434

74.1

7473

-71.

6922

83.

0817

9815

.87

15.6

916

20.5

483

0.98

6-0

.015

-0.0

13-0

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00.

0030

lm01

25l2

5666

73.1

602

-70.

0558

3.08

8091

14.9

814

.72

1976

.560

60.

954

-0.0

16-0

.043

-0.0

010

-0.0

010

0.00

50lm

0454

k243

1579

.701

37-6

5.71

829

3.09

6796

15.7

115

.50

1615

.572

40.

972

-0.0

12-0

.038

-0.0

080

-0.0

17-0

.001

0lm

0172

n244

6875

.397

48-6

8.30

194

3.10

2677

16.4

316

.19

808.

8476

0.89

8-0

.055

-0.1

18-0

.024

-0.0

430.

0040

lm01

13n2

4057

75.4

7999

-69.

6838

13.

1062

4416

.80

16.6

715

91.6

232

0.92

40.

0020

-0.1

29-0

.002

0-0

.089

-0.0

070

lm00

95m

9501

79.5

1951

-69.

8052

73.

1070

1914

.94

14.6

818

18.7

747

0.96

-0.0

020

-0.0

65-0

.006

0-0

.044

0.00

60lm

0346

m33

9283

.107

83-6

7.32

369

3.11

3759

15.8

315

.67

1273

.562

50.

952

-0.0

28-0

.046

-0.0

-0.0

010

0.00

80lm

0026

m14

151

82.6

8247

-70.

1901

53.

1156

0916

.86

16.9

017

71.8

904

0.90

5-0

.034

-0.0

72-0

.003

0-0

.001

00.

016

lm03

34n2

3519

81.4

573

-67.

2570

53.

1197

0115

.80

15.5

511

16.8

374

0.95

7-0

.007

0-0

.067

-0.0

18-0

.032

-0.0

070

lm03

40m

2080

183

.065

23-6

6.39

168

3.12

0686

16.8

816

.66

1592

.639

60.

958

0.00

10-0

.046

0.00

10-0

.017

0.00

10lm

0033

m31

9685

.329

26-6

9.41

801

3.12

2574

15.2

915

.12

2047

.488

20.

945

-0.0

060

-0.0

88-0

.001

0-0

.057

-0.0

lm02

07m

2758

881

.918

38-6

8.87

609

3.12

647

15.8

115

.55

1059

.872

30.

952

0.00

20-0

.062

-0.0

11-0

.038

-0.0

080

lm01

12m

2187

574

.515

57-6

9.55

377

3.13

0149

16.1

115

.97

436.

8064

0.91

8-0

.017

-0.0

87-0

.001

0-0

.013

0.00

40lm

0034

m12

6384

.649

97-6

9.77

342

3.13

4554

16.1

816

.19

1235

.645

50.

976

-0.0

17-0

.023

-0.0

010

-0.0

0.00

10lm

0202

l153

1180

.825

47-6

8.25

012

3.13

9857

15.6

315

.43

2264

.629

80.

89-0

.044

-0.1

6-0

.029

-0.0

740.

0020

lm00

45m

1216

887

.518

45-6

9.87

298

3.14

0267

15.8

915

.63

1822

.763

50.

979

-0.0

17-0

.021

0.00

400.

0060

0.00

20lm

0364

k363

386

.177

55-6

6.97

543.

1419

3816

.07

15.9

112

66.6

517

0.94

4-0

.045

-0.0

65-0

.013

-0.0

260.

0040

lm00

24m

2426

482

.570

5-6

9.88

751

3.14

4057

16.0

315

.96

1916

.594

40.

983

-0.0

14-0

.018

-0.0

010

-0.0

0.00

10lm

0580

m20

047

82.1

2091

-70.

5727

33.

1450

4516

.11

15.8

213

00.5

510

0.88

8-0

.06

-0.1

34-0

.028

-0.0

620.

0020

lm03

45k4

036

83.5

982

-66.

9814

3.15

3308

15.8

915

.70

1317

.521

60.

988

-0.0

060

-0.0

180.

0-0

.009

0-0

.001

0lm

0037

k868

984

.956

45-7

0.16

619

3.15

4552

16.2

816

.17

2404

.553

40.

953

-0.0

77-0

.087

-0.0

3-0

.065

-0.0

060

lm03

33n1

6489

82.4

1114

-66.

8476

73.

1610

615

.07

14.7

323

35.6

579

0.93

7-0

.037

-0.0

81-0

.009

0-0

.021

0.00

10

184


0106

m99

1776

.292

5-7

0.16

055

3.16

128

15.0

214

.83

2169

.755

10.

918

-0.0

33-0

.099

-0.0

11-0

.033

-0.0

lm03

33n1

0485

82.2

1101

-66.

8129

83.

1627

9614

.75

14.4

680

9.68

470.

979

-0.0

16-0

.026

-0.0

010

-0.0

010

-0.0

020

lm03

31n1

3474

82.4

6639

-66.

5854

43.

1636

3616

.21

15.9

922

04.6

430

0.89

2-0

.062

-0.1

42-0

.029

-0.0

630.

0020

lm02

14n2

7117

82.6

9834

-68.

6736

43.

1727

815

.00

14.8

515

32.6

636

0.98

9-0

.016

-0.0

170.

0-0

.0-0

.001

0lm

0397

l969

392

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64-6

7.53

223.

1771

1616

.71

16.5

539

6.83

720.

991

-0.0

28-0

.019

-0.0

020

0.00

10-0

.006

0lm

0092

k175

84*

78.1

4727

-69.

5407

73.

1920

9616

.21

16.1

622

94.6

856

0.98

4-0

.002

0-0

.033

-0.0

010

-0.0

080

-0.0

lm05

43m

3009

374

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89-7

0.97

212

3.19

3725

15.8

515

.74

1467

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30.

968

-0.0

26-0

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-0.0

040

-0.0

060

0.00

10lm

0090

l721

5*78

.075

33-6

9.25

455

3.19

449

16.6

616

.70

2184

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30.

979

-0.0

030

-0.0

41-0

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0-0

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-0.0

010

lm02

23k6

698*

85.2

0794

-68.

0392

33.

2050

2416

.35

16.2

023

96.5

282

0.98

2-0

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0-0

.017

-0.0

020

-0.0

080

0.00

30lm

0240

m16

931

88.3

2281

-67.

7650

23.

2095

9415

.86

15.8

115

94.7

469

0.96

40.

0060

-0.0

48-0

.026

-0.0

090

-0.0

15lm

0287

m42

3973

.699

51-6

7.32

634

3.21

3864

16.2

415

.98

2298

.631

30.

979

0.00

20-0

.027

-0.0

010

-0.0

14-0

.002

0lm

0093

k230

7579

.069

35-6

9.52

412

3.21

4621

15.8

615

.72

1503

.656

30.

926

-0.0

51-0

.093

-0.0

15-0

.033

0.00

50lm

0092

m16

608

78.4

7966

-69.

5337

13.

2195

2314

.56

14.2

917

66.8

702

0.85

9-0

.056

-0.1

66-0

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-0.0

82-0

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0lm

0583

l285

4082

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-71.

1131

13.

2210

615

.63

15.8

012

57.5

922

0.99

4-0

.006

0-0

.009

0-0

.013

-0.0

020

0.00

20lm

0123

l255

6373

.262

4-6

9.69

687

3.22

2946

15.3

015

.10

1071

.742

70.

937

-0.0

090

-0.0

460.

0060

-0.0

010

0.00

50lm

0012

k238

0980

.148

88-6

9.57

091

3.22

4639

16.5

416

.24

2178

.704

70.

929

-0.0

48-0

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-0.0

15-0

.03

-0.0

030

lm02

90l1

8998

73.8

8709

-66.

5420

83.

2248

0515

.32

15.1

511

93.5

685

0.93

4-0

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-0.0

66-0

.002

0-0

.007

00.

0080

lm01

15n1

3901

75.4

074

-69.

9811

73.

2249

2514

.83

14.6

022

65.6

246

0.89

8-0

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-0.1

23-0

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-0.0

280.

0010

lm03

96n1

7800

92.0

6155

-67.

5855

3.23

0491

17.1

616

.98

1982

.664

10.

96-0

.056

-0.0

36-0

.003

0-0

.002

0-0

.004

0lm

0455

k235

3280

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22-6

5.71

217

3.23

3372

15.8

815

.80

1823

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11.

005

-0.0

080

-0.0

17-0

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0-0

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-0.0

020

lm02

85l1

5911

73.1

9292

-67.

2065

3.23

396

16.0

915

.90

2257

.572

70.

904

-0.0

73-0

.147

-0.0

36-0

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-0.0

090

lm02

21n2

2693

85.6

782

-67.

9421

23.

2345

1816

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16.0

914

96.7

246

0.96

9-0

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-0.0

32-0

.001

0-0

.003

0-0

.002

0lm

0305

k407

2*76

.493

98-6

6.97

811

3.23

9846

17.3

317

.22

2081

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50.

995

0.0

-0.0

16-0

.001

0-0

.007

0-0

.001

0lm

0326

k221

1779

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45-6

7.44

853

3.24

0622

16.4

216

.19

1254

.598

90.

966

0.00

30-0

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0.00

30-0

.042

0.00

10lm

0344

k197

5582

.888

9-6

7.08

871

3.24

0951

14.5

114

.30

1941

.775

00.

958

-0.0

16-0

.05

-0.0

040

-0.0

12-0

.002

0lm

0123

m18

261

73.3

5284

-69.

5029

43.

2502

4716

.99

16.9

525

45.6

634

0.93

4-0

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35-0

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-0.0

940.

011

lm02

14n1

2207

82.9

3724

-68.

5812

13.

2529

6916

.15

16.0

442

5.62

910.

977

-0.0

5-0

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-0.0

19-0

.03

0.00

20lm

0207

m82

8082

.002

01-6

8.75

682

3.25

6904

17.1

316

.71

1805

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00.

926

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55-0

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-0.0

1-0

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0.00

80lm

0566

l188

8377

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25-7

1.84

052

3.25

6957

16.8

816

.64

2258

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90.

956

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36-0

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0.00

20-0

.009

0-0

.004

0lm

0106

k149

2175

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21-7

0.19

912

3.26

1387

15.9

215

.76

491.

5882

0.96

8-0

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-0.0

370.

0030

-0.0

030

0.00

80lm

0207

n226

2581

.982

3-6

9.01

378

3.26

4492

15.8

515

.76

2314

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70.

944

-0.0

010

-0.0

730.

0030

-0.0

46-0

.004

0lm

0353

l184

8485

.177

81-6

6.87

581

3.26

9629

16.9

216

.96

1196

.690

20.

936

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53-0

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29-0

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-0.0

030

lm04

35k2

0023

77.2

5556

-65.

6847

63.

2815

9516

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16.6

822

17.8

281

0.99

2-0

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-0.0

32-0

.008

0-0

.03

-0.0

010

lm00

13m

1452

0*81

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11-6

9.48

442

3.28

8232

16.3

016

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1296

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20.

973

0.00

10-0

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-0.0

020

-0.0

290.

0010

lm00

90n1

2880

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.264

13-6

9.28

665

3.28

9332

16.9

216

.93

1887

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70.

971

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020

-0.0

350.

0-0

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0.00

20lm

0114

n174

4474

.338

31-7

0.00

589

3.29

6076

16.1

115

.92

1374

.888

70.

99-0

.005

0-0

.064

-0.0

010

-0.0

53-0

.011

lm02

00l1

8257

80.5

0925

-67.

9272

3.29

6949

14.5

914

.40

1147

.816

20.

891

-0.0

28-0

.13

-0.0

15-0

.043

0.00

80lm

0366

n990

386

.801

93-6

7.52

169

3.30

0117

16.3

916

.21

1978

.622

70.

97-0

.032

-0.0

26-0

.002

00.

0010

-0.0

020

lm04

36l1

9007

76.2

8093

-66.

1938

63.

3011

2315

.18

14.8

719

45.6

937

0.98

-0.0

12-0

.017

-0.0

0.0

-0.0

lm00

93n2

8064

*79

.270

02-6

9.70

178

3.30

5841

917

.47

17.5

413

47.9

240

0.97

7-0

.012

-0.0

420.

0020

-0.0

410.

0040

lm00

91n2

3508

79.2

7861

-69.

3369

63.

3089

8315

.79

15.6

222

08.6

229

0.94

-0.0

17-0

.064

0.0

-0.0

020

0.00

20

185

lm01

57n5

026

72.8

0917

-68.

8809

63.

3113

1916

.72

16.5

818

59.5

651

0.95

9-0

.026

-0.0

36-0

.006

0-0

.007

00.

0080

lm03

35m

1168

382

.155

68-6

7.02

177

3.31

1557

15.5

415

.32

2001

.594

80.

981

-0.0

11-0

.014

-0.0

020

-0.0

010

0.00

70lm

0113

k240

7475

.008

63-6

9.53

223

3.31

7551

16.4

716

.39

1945

.658

30.

936

-0.0

14-0

.081

-0.0

38-0

.02

-0.0

24lm

0193

n144

40*

80.2

8239

-68.

2322

73.

3188

4416

.71

16.6

025

54.7

174

0.97

30.

0020

-0.0

32-0

.002

0-0

.011

0.00

10lm

0343

l222

3983

.744

18-6

6.94

113.

3211

8815

.91

15.7

022

38.6

138

0.96

-0.0

020

-0.0

5-0

.005

0-0

.027

-0.0

040

lm03

60k1

4673

86.1

7458

-66.

3541

13.

3261

8615

.94

15.7

612

73.6

097

0.98

-0.0

24-0

.024

-0.0

58-0

.016

0.02

1lm

0353

l258

2385

.540

38-6

6.92

105

3.32

6584

16.8

316

.73

1960

.718

40.

975

-0.0

040

-0.0

34-0

.004

0-0

.017

-0.0

lm05

51k1

3555

76.3

388

-70.

5525

53.

3341

9416

.01

15.7

570

5.74

910.

989

-0.0

030

-0.0

15-0

.0-0

.009

00.

0010

lm01

26m

1555

472

.529

38-7

0.20

161

3.35

0086

15.5

615

.42

2198

.780

00.

9-0

.011

-0.1

57-0

.007

0-0

.094

-0.0

090

lm03

17n1

5681

78.6

9001

-67.

5630

83.

3593

7115

.13

14.9

820

31.4

960

0.89

1-0

.018

-0.1

31-0

.01

-0.0

340.

0080

lm02

96n1

1158

74.3

0055

-67.

5285

13.

3593

7716

.37

16.1

816

29.5

409

0.94

7-0

.017

-0.0

97-0

.018

-0.0

64-0

.01

lm03

35n9

834*

82.4

8561

-67.

1600

53.

3629

4816

.85

16.5

716

54.5

282

0.97

9-0

.01

-0.0

37-0

.006

0-0

.031

-0.0

lm05

41n1

3040

74.5

9473

-70.

7119

63.

3671

816

.78

16.5

312

59.5

290

0.98

6-0

.006

0-0

.022

-0.0

060

-0.0

16-0

.001

0lm

0157

n615

772

.818

82-6

8.88

963.

3700

7415

.17

15.0

315

29.5

687

0.95

9-0

.019

-0.0

44-0

.002

0-0

.013

0.00

20lm

0023

k426

583

.104

66-6

9.42

709

3.37

023

15.6

615

.44

1538

.652

30.

917

-0.0

080

-0.1

44-0

.005

0-0

.086

-0.0

020

lm02

16m

2662

4*82

.801

84-6

8.87

256

3.37

1126

17.3

117

.25

1659

.548

60.

949

-0.0

060

-0.0

85-0

.006

0-0

.066

-0.0

040

lm03

66m

8525

*86

.626

4-6

7.35

921

3.37

1884

16.9

316

.81

2000

.592

10.

957

-0.0

020

-0.0

66-0

.001

0-0

.051

0.00

20lm

0342

k173

2182

.663

93-6

6.74

441

3.37

3808

15.4

315

.23

1468

.674

70.

959

-0.0

040

-0.0

5-0

.005

0-0

.021

0.00

30lm

0184

l243

4976

.660

06-6

8.65

452

3.37

5765

15.5

715

.44

1247

.558

70.

977

-0.0

41-0

.031

-0.0

41-0

.019

0.00

60lm

0345

k154

8983

.545

25-6

7.05

712

3.37

8755

15.3

115

.13

1968

.654

70.

98-0

.006

0-0

.024

-0.0

040

-0.0

080

0.00

10lm

0036

m19

194*

84.5

0262

-70.

2262

83.

3817

4217

.26

17.2

114

54.7

138

0.96

30.

0010

-0.0

31-0

.001

0-0

.017

-0.0

010

lm04

46k2

0008

77.8

7865

-66.

0485

93.

3820

6516

.67

16.5

421

83.7

359

0.99

1-0

.027

-0.0

150.

00.

0-0

.005

0lm

0180

l204

43*

77.0

89-6

7.93

533.

3835

0216

.75

16.6

011

98.6

496

0.97

3-0

.001

0-0

.039

-0.0

020

-0.0

160.

0010

lm05

95k6

058*

84.5

6346

-71.

1923

73.

3862

717

.22

17.1

812

81.6

027

0.97

8-0

.004

0-0

.037

-0.0

020

-0.0

210.

0020

lm00

93n3

3808

*79

.337

19-6

9.73

054

3.39

0984

17.0

516

.98

1078

.784

41.

002

-0.0

-0.0

3-0

.001

0-0

.018

-0.0

030

lm03

65n2

3864

87.6

3119

-67.

2635

63.

4003

0716

.92

16.6

916

57.5

424

0.94

-0.0

37-0

.069

-0.0

070

-0.0

160.

0030

lm00

22k4

406

81.9

1673

-69.

4356

63.

4039

9715

.00

14.7

816

53.5

704

0.89

-0.0

35-0

.135

-0.0

23-0

.057

0.00

80lm

0333

n183

9282

.354

35-6

6.85

994

3.40

4099

16.7

516

.59

2511

.828

50.

882

-0.0

55-0

.147

-0.0

29-0

.06

0.00

60lm

0030

l133

5183

.919

36-6

9.30

042

3.40

8736

14.5

614

.40

1763

.815

40.

9-0

.024

-0.1

21-0

.009

0-0

.032

0.00

30lm

0331

m23

548

82.1

2763

-66.

4002

13.

4128

8415

.34

15.0

822

49.8

462

0.97

1-0

.024

-0.0

30.

0-0

.001

00.

0030

lm00

30l4

784

84.1

129

-69.

2377

3.41

3421

15.7

915

.86

1879

.663

90.

981

-0.0

010

-0.0

31-0

.002

0-0

.022

-0.0

030

lm01

15k1

0662

75.0

248

-69.

8139

63.

4163

7516

.49

16.4

311

22.7

615

0.91

4-0

.053

-0.0

94-0

.018

-0.0

310.

0040

lm02

94m

1493

374

.258

77-6

7.04

443.

4207

0916

.74

16.6

819

47.6

718

0.96

-0.0

17-0

.035

0.00

20-0

.001

00.

0040

lm05

84n1

8193

82.0

8746

-71.

4121

33.

4265

1815

.10

14.9

415

28.6

761

0.86

6-0

.054

-0.1

69-0

.027

-0.0

860.

0020

lm04

66n1

3702

81.5

3741

-66.

1499

23.

4327

3414

.40

14.6

017

90.8

409

0.92

2-0

.017

-0.0

81-0

.011

-0.0

020

-0.0

lm02

85m

1334

973

.533

75-6

7.03

497

3.43

8956

16.3

016

.12

782.

6400

0.93

5-0

.009

0-0

.104

-0.0

060

-0.0

62-0

.002

0lm

0175

k304

0175

.837

32-6

8.52

178

3.44

0068

15.8

715

.79

1200

.650

30.

974

-0.0

23-0

.025

-0.0

020

0.0

0.00

10lm

0105

l704

777

.006

14-6

9.97

644

3.44

2404

16.9

216

.76

762.

6691

0.98

-0.0

030

-0.0

3-0

.022

-0.0

12-0

.007

0lm

0466

l185

0181

.258

29-6

6.18

943

3.44

5012

15.8

715

.85

2132

.831

50.

927

-0.0

26-0

.072

-0.0

010

-0.0

070

0.00

60lm

0187

l139

41*

77.9

9728

-68.

9502

43.

4477

6217

.36

17.4

949

6.67

190.

963

0.00

70-0

.04

-0.0

010

-0.0

190.

0020

lm02

25k2

6953

85.2

8308

-68.

5165

53.

4528

7916

.43

16.4

018

83.7

115

0.89

6-0

.06

-0.1

3-0

.027

-0.0

530.

0040

186


0541

n183

2074

.751

07-7

0.75

661

3.45

9966

16.7

016

.47

1067

.741

30.

932

-0.0

47-0

.089

-0.0

16-0

.035

-0.0

020

lm01

75n2

1939

*76

.460

1-6

8.62

454

3.46

2514

16.2

516

.08

1453

.844

30.

968

0.00

10-0

.034

0.0

-0.0

040

0.00

30lm

0343

k222

9983

.822

34-6

6.73

423

3.46

6279

15.5

215

.28

933.

5105

0.98

7-0

.003

0-0

.023

-0.0

020

-0.0

080

-0.0

020

lm00

33k4

809

84.8

9519

-69.

4277

3.46

8732

16.7

716

.76

1970

.622

50.

973

-0.0

15-0

.019

-0.0

030

0.00

100.

0030

lm01

66l1

2483

73.0

8311

-68.

9403

53.

4687

7815

.42

15.2

521

98.6

216

0.97

7-0

.018

-0.0

240.

0020

0.00

400.

0040

lm02

21n7

928

85.8

9611

-67.

8446

73.

4688

0215

.24

14.9

421

92.8

314

0.99

5-0

.005

0-0

.02

-0.0

11-0

.014

-0.0

lm03

21m

6695

80.5

1609

-66.

2821

13.

4697

216

.11

15.7

077

6.75

600.

979

-0.0

020

-0.0

37-0

.005

0-0

.02

-0.0

040

lm02

02l2

4207

80.6

5683

-68.

3071

23.

4721

8616

.85

16.7

518

19.7

651

0.96

4-0

.026

-0.0

33-0

.001

00.

0030

0.00

30lm

0105

n273

6577

.646

79-7

0.05

544

3.47

6907

16.4

716

.26

1992

.549

60.

96-0

.028

-0.0

310.

00.

0010

0.00

50lm

0681

m21

371

77.6

2627

-71.

9858

13.

4869

6416

.07

15.8

115

91.6

457

0.98

-0.0

18-0

.021

-0.0

010

0.00

100.

0010

lm01

77l9

536

76.0

3674

-68.

9198

43.

4910

2616

.79

16.6

039

0.76

270.

975

-0.0

080

-0.0

26-0

.002

0-0

.014

-0.0

030

lm01

57n2

0802

72.5

0246

-69.

0025

13.

4917

6616

.24

16.0

614

94.5

699

0.96

8-0

.023

-0.0

39-0

.003

00.

0020

-0.0

030

lm03

44m

8000

83.1

3842

-67.

0082

23.

4962

8815

.36

15.1

422

51.6

815

0.95

60.

0070

-0.0

650.

0010

-0.0

4-0

.006

0lm

0195

m24

877

80.0

4894

-68.

4935

33.

5080

0816

.80

16.7

574

1.79

940.

974

-0.0

34-0

.043

-0.0

060

-0.0

-0.0

020

lm01

84l1

5997

77.0

3259

-68.

6054

73.

5092

4615

.72

15.5

313

88.8

150

0.97

3-0

.008

0-0

.031

-0.0

030

-0.0

14-0

.0lm

0180

l248

3676

.772

16-6

7.96

542

3.51

3017

15.3

715

.17

1555

.622

40.

972

-0.0

14-0

.022

0.00

200.

0010

0.00

60lm

0024

k235

11*

81.6

07-6

9.77

156

3.52

2356

16.2

816

.16

523.

6086

0.98

7-0

.005

0-0

.015

-0.0

020

-0.0

10.

0020

lm00

91k1

4479

78.9

015

-69.

1394

63.

5247

5916

.67

16.4

718

44.7

458

0.97

1-0

.086

-0.1

04-0

.025

-0.0

59-0

.003

0lm

0021

n294

3583

.654

34-6

9.36

785

3.53

1735

15.5

215

.24

2144

.805

10.

989

-0.0

080

-0.0

14-0

.006

0-0

.009

0-0

.001

0lm

0013

n300

0881

.286

76-6

9.71

265

3.53

8905

15.8

715

.70

1467

.725

60.

974

-0.0

22-0

.022

0.00

100.

0010

0.00

30lm

0337

k233

4281

.890

47-6

7.46

495

3.54

3441

14.9

814

.73

1442

.816

70.

985

-0.0

43-0

.03

-0.0

16-0

.028

-0.0

040

lm03

05m

2705

276

.829

96-6

7.11

363

3.54

5493

15.9

815

.75

1082

.832

80.

925

-0.0

46-0

.092

-0.0

16-0

.035

0.00

10lm

0303

k138

61*

76.7

6351

-66.

6787

93.

5456

917

.20

17.1

121

87.7

137

0.98

-0.0

010

-0.0

280.

0010

-0.0

12-0

.001

0lm

0095

n308

4779

.720

56-7

0.07

168

3.54

6722

16.9

116

.72

325.

8327

0.91

1-0

.094

-0.1

42-0

.047

-0.0

790.

0040

lm03

43k1

3626

83.6

8195

-66.

6821

13.

5491

3415

.99

15.8

014

63.7

628

0.93

1-0

.039

-0.0

81-0

.007

0-0

.021

0.00

30lm

0182

n124

29*

77.4

1051

-68.

2277

13.

5511

7817

.52

17.4

310

88.7

063

0.97

-0.0

030

-0.0

44-0

.002

0-0

.027

-0.0

040

lm05

56k5

652

75.1

5243

-71.

5250

83.

5531

2216

.62

16.5

212

65.5

806

0.95

8-0

.03

-0.0

54-0

.0-0

.005

00.

0030

lm03

44n2

4008

*83

.255

17-6

7.26

013.

5553

4215

.85

15.6

217

64.8

820

0.97

9-0

.001

0-0

.022

-0.0

030

-0.0

050

0.00

10lm

0090

m44

7978

.380

06-6

9.08

046

3.55

8236

16.6

516

.46

1342

.933

40.

968

-0.0

29-0

.04

-0.0

060

-0.0

110.

0010

lm02

30k5

872*

86.0

5593

-67.

8259

83.

5617

1816

.97

16.9

353

9.57

150.

956

-0.0

020

-0.0

42-0

.001

0-0

.014

0.00

20lm

0344

l215

9682

.796

21-6

7.25

583

3.58

4081

16.9

616

.82

1067

.803

00.

978

-0.0

28-0

.025

-0.0

0.00

200.

0070

lm03

41l2

1911

83.4

1158

-66.

5794

43.

5847

1616

.17

16.1

419

37.7

144

0.92

3-0

.065

-0.1

04-0

.029

-0.0

53-0

.001

0lm

0343

n204

4783

.998

97-6

6.93

869

3.58

5424

15.4

915

.20

507.

5786

0.98

7-0

.008

0-0

.019

-0.0

050

-0.0

090

-0.0

010

lm02

87m

1507

073

.365

58-6

7.40

108

3.58

6708

16.8

816

.78

2262

.847

00.

966

-0.0

31-0

.019

-0.0

030

0.00

400.

0090

lm03

74m

1672

4*88

.408

74-6

7.07

084

3.59

3318

16.8

016

.65

1784

.833

80.

978

-0.0

040

-0.0

29-0

.006

0-0

.018

-0.0

030

lm01

21l2

2345

73.0

4166

-69.

3346

23.

5953

9216

.67

16.5

214

24.7

830

0.94

-0.0

38-0

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-0.0

060

-0.0

150.

0030

lm03

23n1

1823

*80

.603

03-6

6.81

992

3.59

9714

16.6

916

.47

2025

.511

40.

982

-0.0

070

-0.0

19-0

.003

0-0

.007

0-0

.0lm

0110

l216

1374

.046

57-6

9.35

041

3.60

6183

15.5

815

.34

708.

8980

0.96

70.

0030

-0.0

640.

0030

-0.0

36-0

.002

0lm

0343

l158

4083

.656

09-6

6.85

268

3.60

9432

14.8

514

.61

540.

5105

0.92

4-0

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-0.0

670.

0-0

.004

00.

01lm

0340

l679

182

.663

04-6

6.45

076

3.61

2113

16.8

716

.78

1267

.593

00.

875

-0.1

07-0

.158

-0.0

5-0

.079

0.00

90lm

0366

l773

486

.224

26-6

7.50

409

3.61

3542

16.6

116

.45

1824

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50.

956

-0.0

12-0

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-0.0

060

-0.0

49-0

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187

lm01

63l2

4856

74.1

3186

-68.

2975

93.

6183

4716

.37

16.2

923

89.5

005

0.98

4-0

.001

0-0

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-0.0

060

-0.0

030

-0.0

010

lm00

15n3

0492

81.2

8868

-70.

0728

63.

6255

1316

.49

16.3

515

32.6

440

0.97

1-0

.008

0-0

.06

-0.0

070

-0.0

420.

0040

lm00

93k2

7461

79.2

0581

-69.

5460

83.

6282

9915

.62

15.4

393

1.49

890.

96-0

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0-0

.051

-0.0

050

-0.0

26-0

.001

0lm

0091

l251

5879

.110

48-6

9.34

246

3.63

4311

15.2

815

.24

1441

.748

90.

927

-0.0

3-0

.077

-0.0

15-0

.03

0.00

40lm

0560

m17

742

77.7

2478

-70.

5573

93.

6409

8916

.33

16.1

378

8.76

770.

956

-0.0

29-0

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0.00

10-0

.001

00.

0040

lm00

13m

2236

381

.343

14-6

9.52

733

3.64

6111

16.7

416

.73

1784

.774

80.

98-0

.015

-0.0

15-0

.00.

0040

0.00

40lm

0225

n759

285

.637

34-6

8.54

787

3.65

2101

15.7

415

.52

1108

.850

10.

948

-0.0

080

-0.0

86-0

.008

0-0

.063

0.00

60lm

0184

l495

7*76

.909

69-6

8.53

939

3.65

273

16.5

316

.62

1059

.851

20.

989

-0.0

020

-0.0

270.

0-0

.014

0.00

10lm

0303

n178

56*

76.9

238

-66.

8528

53.

6554

216

.54

16.3

212

01.5

979

0.98

3-0

.003

0-0

.026

-0.0

030

-0.0

190.

0010

lm03

43l1

6325

83.4

0523

-66.

8571

43.

6555

3315

.13

14.8

923

44.6

483

0.95

9-0

.002

0-0

.058

-0.0

14-0

.038

0.00

70lm

0184

k134

0976

.689

95-6

8.43

575

3.65

9249

16.1

616

.04

2057

.484

60.

969

-0.0

28-0

.032

-0.0

020

-0.0

090

0.00

20lm

0343

k228

5983

.586

19-6

6.73

907

3.66

4324

15.3

015

.07

1901

.848

30.

847

-0.0

38-0

.18

-0.0

21-0

.057

0.02

5lm

0207

m69

63*

81.8

4109

-68.

7502

73.

6773

3215

.35

15.1

213

74.9

246

0.94

-0.0

020

-0.0

8-0

.0-0

.023

-0.0

lm01

00l2

2336

*76

.063

4-6

9.35

643

3.67

9464

16.8

216

.85

2294

.664

70.

985

-0.0

010

-0.0

26-0

.001

0-0

.018

0.0

lm05

65k6

340

78.4

8164

-71.

1866

3.69

0546

14.7

914

.60

1142

.665

60.

97-0

.019

-0.0

3-0

.0-0

.001

00.

0030

lm00

33n1

8886

85.4

3758

-69.

6679

3.69

4692

14.7

014

.44

1950

.619

30.

987

-0.0

010

-0.0

15-0

.003

0-0

.003

00.

0010

lm03

44l1

9313

82.7

1621

-67.

2402

73.

6959

3515

.18

14.9

620

17.5

704

0.96

70.

0020

-0.0

51-0

.02

-0.0

2-0

.012

lm00

13n8

661

81.3

1174

-69.

6034

63.

7145

2616

.00

15.9

253

2.51

850.

971

-0.0

-0.0

37-0

.002

0-0

.02

0.0

lm00

33m

1706

385

.307

12-6

9.50

278

3.71

8525

14.8

414

.67

388.

8496

0.98

4-0

.01

-0.0

13-0

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0-0

.001

00.

0010

lm03

31n1

614

82.1

504

-66.

4287

83.

7206

916

.76

16.5

914

42.8

167

0.99

2-0

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-0.0

11-0

.013

-0.0

10.

0020

lm01

25n2

3449

73.4

2151

-70.

0405

43.

7387

1415

.31

15.1

119

76.5

606

0.88

1-0

.06

-0.1

51-0

.027

-0.0

70.

0030

lm05

51m

2068

1*76

.877

3-7

0.57

786

3.74

0874

17.6

117

.43

1838

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20.

961

0.00

60-0

.063

0.00

20-0

.047

0.0

lm02

83n1

5751

73.6

2331

-66.

8483

3.74

2176

16.6

216

.38

2255

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00.

961

-0.0

2-0

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-0.0

19-0

.044

-0.0

070

lm04

24n5

194

74.8

0668

-65.

7366

43.

7442

2614

.62

14.4

211

83.6

480

0.89

7-0

.018

-0.1

18-0

.018

-0.0

460.

0080

lm00

13n3

2504

81.2

7858

-69.

7254

93.

7450

0816

.28

16.1

712

66.5

735

0.98

7-0

.01

-0.0

13-0

.002

00.

0010

0.00

40lm

0291

l489

175

.000

36-6

6.42

614

3.75

1829

15.4

715

.14

2257

.860

50.

913

-0.0

41-0

.109

-0.0

15-0

.036

0.00

70lm

0027

k382

3*82

.861

65-7

0.13

678

3.76

1414

16.1

916

.10

511.

5406

0.95

8-0

.014

-0.0

39-0

.003

0-0

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00.

0030

lm01

01n2

5168

77.6

1906

-69.

3465

93.

7734

0815

.86

15.5

650

8.57

180.

977

0.01

2-0

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-0.0

11-0

.02

-0.0

14lm

0207

k168

3781

.734

28-6

8.80

786

3.77

5084

15.7

615

.48

428.

6362

1.0

-0.0

2-0

.003

0-0

.001

0-0

.006

0-0

.001

0lm

0092

m24

157

78.2

7531

-69.

5762

33.

7795

2815

.91

15.7

624

60.9

331

0.99

3-0

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-0.0

13-0

.01

-0.0

160.

0010

lm02

14n8

614

82.9

6898

-68.

5586

93.

7858

4516

.52

16.4

422

42.6

112

0.97

4-0

.009

0-0

.012

-0.0

51-0

.014

-0.0

21lm

0333

k491

481

.804

24-6

6.62

823.

7902

6915

.57

15.3

818

95.6

174

0.98

5-0

.006

0-0

.011

-0.0

18-0

.003

0-0

.009

0lm

0266

n880

892

.493

46-6

9.05

534

3.79

1436

16.6

116

.37

503.

7005

0.93

3-0

.053

-0.0

69-0

.009

0-0

.018

0.01

1lm

0020

m22

505

82.6

2036

-69.

1940

73.

7916

9115

.68

15.5

522

97.7

436

0.92

1-0

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7-0

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00.

012

lm02

85k2

2500

73.2

004

-67.

1005

13.

7927

815

.83

15.7

022

58.7

408

0.95

8-0

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-0.0

410.

0010

-0.0

030

0.00

50lm

0030

l159

0484

.160

62-6

9.32

033

3.79

7121

15.2

115

.21

2312

.749

10.

977

-0.0

11-0

.017

-0.0

0.0

0.00

60lm

0555

m16

884

76.5

4721

-71.

2783

63.

8007

6716

.44

16.3

019

87.5

504

0.90

7-0

.04

-0.1

15-0

.018

-0.0

39-0

.001

0lm

0550

m52

1275

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54-7

0.48

438

3.80

1039

15.8

815

.55

2204

.602

10.

974

-0.0

040

-0.0

35-0

.006

0-0

.017

0.00

10lm

0257

l893

191

.105

99-6

8.92

443

3.81

0748

15.5

315

.19

2264

.805

10.

933

0.01

-0.1

06-0

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0-0

.074

0.01

lm05

83l2

8572

82.3

6022

-71.

1147

13.

8228

9516

.57

16.5

512

66.6

017

0.98

4-0

.002

0-0

.024

-0.0

-0.0

14-0

.0lm

0050

n162

62*

88.3

4579

-69.

3054

73.

8284

881

16.8

516

.71

390.

7966

0.95

10.

018

-0.0

940.

0090

-0.0

840.

0010

188


0125

k810

672

.823

49-6

9.80

212

3.84

3898

15.8

615

.80

1888

.570

70.

961

-0.0

27-0

.053

-0.0

080

-0.0

18-0

.001

0lm

0367

l133

3187

.241

67-6

7.55

966

3.84

6704

16.4

916

.28

1804

.860

10.

953

-0.0

49-0

.057

-0.0

080

-0.0

140.

0050

lm01

12l2

2418

*74

.077

03-6

9.69

282

3.85

1004

17.1

817

.04

1804

.762

10.

957

-0.0

010

-0.0

720.

0020

-0.0

660.

011

lm00

90n3

0909

78.3

2119

-69.

3889

43.

8520

9715

.73

15.6

417

11.9

284

0.98

8-0

.01

-0.0

18-0

.005

0-0

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-0.0

lm00

30l1

1056

84.2

0283

-69.

2832

93.

8535

5815

.33

15.1

443

3.67

990.

95-0

.016

-0.0

37-0

.056

-0.0

020

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21lm

0090

k101

70*

78.1

2455

-69.

1211

63.

8547

9616

.56

16.5

022

02.6

635

0.98

2-0

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0-0

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-0.0

040

-0.0

080

0.00

10lm

0175

n288

6976

.495

99-6

8.66

344

3.85

5031

16.3

716

.03

381.

8370

0.93

4-0

.039

-0.0

85-0

.011

-0.0

310.

0lm

0020

k155

8182

.066

69-6

9.16

523

3.86

3955

14.9

714

.77

1076

.890

30.

966

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030

-0.0

490.

0-0

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010

lm00

26n7

027

82.3

5945

-70.

3028

53.

8704

8516

.17

16.2

866

5.84

440.

936

-0.0

44-0

.091

-0.0

28-0

.046

0.00

50lm

0024

k652

981

.831

58-6

9.68

507

3.87

2692

16.3

516

.17

931.

4717

0.94

9-0

.049

-0.0

65-0

.009

0-0

.02

-0.0

020

lm01

17m

1273

075

.629

58-7

0.18

216

3.87

3811

16.3

416

.22

2208

.749

80.

912

-0.1

-0.1

31-0

.05

-0.0

84-0

.004

0lm

0177

l975

475

.870

27-6

8.92

221

3.89

0098

15.4

814

.96

2300

.633

20.

917

-0.0

57-0

.12

-0.0

2-0

.058

0.00

60lm

0362

n518

286

.733

8-6

6.78

992

3.89

1688

16.1

615

.96

892.

6980

0.92

8-0

.009

0-0

.114

-0.0

080

-0.0

86-0

.01

lm01

12m

2139

474

.533

96-6

9.55

076

3.89

5853

15.3

515

.21

2389

.516

40.

96-0

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36-0

.001

00.

00.

0010

lm00

10l2

3506

80.0

8352

-69.

3623

63.

9040

7716

.22

16.1

214

92.6

657

0.95

3-0

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-0.0

29-0

.001

00.

0030

0.00

30lm

0121

l272

0873

.122

09-6

9.36

341

3.90

7531

15.7

515

.63

1821

.706

40.

967

-0.0

15-0

.024

-0.0

45-0

.007

00.

019

lm03

54l2

3952

84.2

7038

-67.

2700

33.

9094

0415

.83

15.5

412

90.5

659

0.90

4-0

.078

-0.1

24-0

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-0.0

720.

0060

lm03

45n2

7198

84.2

7032

-67.

2701

13.

9094

7415

.70

15.4

610

59.9

019

0.89

6-0

.073

-0.1

24-0

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-0.0

550.

0050

lm00

55k6

835

88.9

7061

-69.

7922

3.91

5014

16.4

516

.36

510.

6379

0.95

9-0

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-0.0

340.

00.

0010

0.00

30lm

0165

n592

874

.569

77-6

8.53

736

3.92

6326

15.0

214

.82

1093

.774

00.

899

-0.0

35-0

.13

-0.0

14-0

.04

0.00

30lm

0120

m20

609

72.7

3139

-69.

1775

73.

9316

6516

.82

16.6

622

41.5

917

0.87

1-0

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-0.1

87-0

.035

-0.0

70.

0010

lm02

87m

2203

673

.601

84-6

7.44

495

3.94

5121

16.2

016

.03

2074

.934

10.

896

-0.0

81-0

.158

-0.0

41-0

.092

-0.0

050

lm01

87m

9985

78.1

6571

-68.

7674

83.

9453

1916

.76

16.5

984

2.65

350.

931

-0.0

77-0

.106

-0.0

3-0

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-0.0

040

lm03

45k9

648

83.7

3768

-67.

0169

93.

9482

3115

.44

15.2

419

55.7

165

0.96

6-0

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-0.0

320.

0010

0.00

300.

0010

lm04

43l6

372

78.8

1883

-65.

5297

43.

9491

8516

.65

16.4

712

67.5

402

0.96

2-0

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-0.0

52-0

.009

0-0

.017

-0.0

020

lm02

00l6

074

80.5

7817

-67.

8390

13.

9504

7815

.89

15.6

512

73.5

276

0.98

5-0

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0-0

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-0.0

010

-0.0

2-0

.003

0lm

0377

l548

189

.056

96-6

7.56

23.

9515

4116

.72

16.4

915

72.8

209

0.93

3-0

.041

-0.0

65-0

.008

0-0

.014

0.00

70lm

0091

m37

97*

79.4

4924

-69.

0710

83.

9545

17.1

316

.93

490.

7461

0.94

-0.0

010

-0.1

37-0

.006

0-0

.095

-0.0

030

lm03

31k2

1866

81.8

5552

-66.

3928

83.

9591

1316

.76

16.5

315

31.6

643

0.98

2-0

.015

-0.0

12-0

.041

-0.0

080

-0.0

19lm

0015

k865

880

.912

97-6

9.80

448

3.95

9962

16.1

716

.32

521.

5561

0.98

7-0

.011

-0.0

16-0

.001

00.

0010

0.00

10lm

0364

l141

9386

.158

85-6

7.20

871

3.95

9976

16.5

316

.39

2018

.584

60.

937

-0.0

52-0

.066

-0.0

12-0

.032

0.00

30lm

0331

l260

4281

.984

27-6

6.57

005

3.96

9029

15.9

515

.81

1805

.887

70.

871

-0.0

59-0

.153

-0.0

38-0

.062

0.01

3lm

0300

m22

019

75.9

5469

-66.

3924

63.

9865

2916

.62

16.3

615

49.6

231

0.97

3-0

.003

0-0

.009

0-0

.056

-0.0

2-0

.029

lm03

17k7

631

78.3

3439

-67.

3594

33.

9901

2615

.61

15.3

321

41.8

302

0.99

-0.0

-0.0

22-0

.025

-0.0

050

0.02

lm01

84n2

6760

77.4

8968

-68.

6582

34.

0224

2815

.38

15.2

015

47.6

132

0.87

7-0

.058

-0.1

68-0

.024

-0.0

710.

0080

lm00

12n4

832

80.2

8006

-69.

5904

4.02

7903

16.6

516

.30

2162

.751

60.

977

-0.0

49-0

.045

-0.0

040

-0.0

030

0.00

90lm

0021

l453

0*82

.869

46-6

9.23

199

4.03

7538

715

.06

14.8

016

21.5

653

0.91

7-0

.008

0-0

.11

-0.0

030

-0.0

370.

0020

lm06

00k2

5018

85.5

8539

-70.

6266

74.

0466

0714

.85

14.7

520

56.4

893

0.96

7-0

.019

-0.0

330.

0010

-0.0

0.00

40lm

0317

k229

7878

.156

81-6

7.47

264.

0519

1614

.67

14.4

111

45.6

945

0.97

-0.0

23-0

.027

0.00

10-0

.00.

0050

lm00

22k4

055

81.9

6774

-69.

4334

64.

0549

5116

.23

16.0

919

34.7

295

0.89

-0.0

58-0

.124

-0.0

25-0

.046

0.00

80lm

0224

m12

405

84.6

8721

-68.

4285

14.

0619

2816

.41

16.3

214

53.8

637

0.92

-0.0

34-0

.091

-0.0

1-0

.023

0.00

50

189

lm03

87l8

658

90.6

794

-67.

5258

44.

0647

3116

.82

16.6

216

54.5

882

0.98

3-0

.021

-0.0

20.

0010

0.0

0.00

20lm

0101

k237

8477

.111

18-6

9.20

004

4.06

9483

15.6

615

.48

491.

5882

0.97

-0.0

21-0

.012

-0.0

040

0.00

200.

012

lm02

23n1

9693

85.5

091

-68.

2701

54.

0754

5515

.32

15.1

416

61.5

381

0.93

9-0

.047

-0.0

96-0

.022

-0.0

440.

0030

lm01

74k1

6339

75.1

3969

-68.

4516

84.

0809

4815

.44

15.2

812

12.6

916

0.94

7-0

.01

-0.0

390.

0010

0.00

100.

015

lm02

43m

4872

89.4

1949

-68.

078

4.08

1141

15.2

214

.96

950.

4929

0.99

9-0

.012

-0.0

030

-0.0

010

-0.0

010

-0.0

040

lm03

43n2

1737

83.9

8722

-66.

8859

94.

0864

9214

.66

14.3

694

7.51

930.

988

-0.0

090

-0.0

14-0

.002

0-0

.005

0-0

.001

0lm

0357

k750

085

.565

95-6

7.35

875

4.09

4591

15.0

214

.77

1263

.623

40.

923

-0.0

25-0

.072

-0.0

030

-0.0

060

0.01

3lm

0691

m10

693

79.5

6567

-71.

9110

64.

0973

8916

.28

16.0

318

27.7

694

0.92

-0.0

48-0

.086

-0.0

11-0

.021

0.00

70lm

0337

k108

4782

.019

22-6

7.37

806

4.11

5728

14.8

514

.60

1875

.667

80.

889

-0.0

5-0

.165

-0.0

26-0

.07

0.00

70lm

0170

n123

0575

.522

14-6

7.88

198

4.11

6486

15.8

015

.58

1962

.691

10.

92-0

.011

-0.1

22-0

.005

0-0

.071

-0.0

030

lm05

85m

1341

982

.982

42-7

1.22

553

4.11

8108

16.8

516

.53

759.

8288

0.98

6-0

.062

-0.0

32-0

.026

-0.0

360.

0010

lm02

06n2

6379

80.9

7014

-69.

0272

24.

1276

6514

.78

14.4

517

88.8

132

0.91

2-0

.033

-0.1

13-0

.008

0-0

.04

0.0

lm03

43k2

1879

83.5

8343

-66.

7333

24.

1631

7915

.89

15.6

818

50.6

457

0.99

1-0

.004

0-0

.019

-0.0

040

-0.0

12-0

.001

0lm

0344

l216

5682

.788

69-6

7.25

619

4.16

4156

15.5

115

.30

1604

.622

40.

989

-0.0

050

-0.0

23-0

.009

0-0

.013

0.00

20lm

0101

k179

6876

.824

63-6

9.16

519

4.17

6462

15.3

315

.19

1792

.798

40.

868

-0.0

69-0

.173

-0.0

36-0

.079

0.00

70lm

0466

l160

7781

.342

82-6

6.16

931

4.17

9091

14.1

414

.13

1547

.682

50.

956

-0.0

050

-0.0

180.

0030

-0.0

060

0.00

40lm

0020

k869

182

.099

51-6

9.11

761

4.17

9714

.77

14.5

594

7.47

960.

966

-0.0

050

-0.0

37-0

.003

0-0

.015

0.00

20lm

0344

m20

206

82.9

4425

-67.

0883

54.

1814

1215

.24

15.0

715

67.7

128

0.93

2-0

.016

-0.0

550.

0020

0.00

100.

013

lm01

25n6

068

73.3

3501

-69.

9366

94.

1877

5615

.92

15.7

922

25.5

710

0.93

-0.0

33-0

.076

-0.0

1-0

.02

0.00

70lm

0110

m10

393

74.4

2887

-69.

1106

24.

1926

2516

.24

16.0

812

69.5

361

0.93

-0.0

74-0

.096

-0.0

27-0

.049

0.00

20lm

0103

k263

1177

.042

34-6

9.54

322

4.20

3111

16.3

016

.26

1891

.626

10.

9-0

.057

-0.1

16-0

.034

-0.0

510.

013

lm03

47n6

886*

84.0

5524

-67.

4972

24.

2108

5816

.07

15.9

712

91.5

689

0.98

4-0

.01

-0.0

4-0

.007

0-0

.034

-0.0

040

lm03

66l1

6862

86.2

1569

-67.

5757

74.

2325

2715

.74

15.5

517

60.8

354

0.98

6-0

.015

-0.0

14-0

.001

0-0

.001

0-0

.001

0lm

0346

k238

2582

.786

51-6

7.48

403

4.24

9299

14.9

014

.67

385.

6731

0.95

5-0

.014

-0.0

66-0

.034

-0.0

29-0

.019

lm01

77l1

6525

76.1

8763

-68.

9676

74.

2535

7716

.56

16.4

012

74.5

110

0.96

-0.0

050

-0.0

45-0

.001

0-0

.02

0.00

20lm

0313

m25

631

78.7

6599

-66.

7502

44.

2639

3416

.40

16.1

275

5.72

540.

983

-0.0

080

-0.0

14-0

.004

0-0

.01

0.00

20lm

0466

n219

5981

.513

27-6

6.21

313

4.27

3267

16.2

416

.04

1262

.522

70.

971

-0.0

24-0

.038

0.00

10-0

.001

00.

0030

lm00

94l2

5321

78.0

1319

-70.

0595

74.

2749

8216

.48

16.5

118

91.6

482

0.97

1-0

.016

-0.0

330.

0010

0.00

30-0

.001

0lm

0122

l155

8172

.060

89-6

9.66

111

4.28

4122

15.7

015

.51

2257

.566

90.

984

-0.0

050

-0.0

2-0

.005

0-0

.004

00.

0010

lm01

13l2

8118

*75

.282

82-6

9.70

783

4.30

563

16.2

616

.21

2516

.765

40.

973

-0.0

060

-0.0

26-0

.005

0-0

.002

00.

0lm

0376

m47

7388

.481

33-6

7.33

126

4.30

6026

15.9

115

.74

512.

7044

0.98

6-0

.018

-0.0

090

0.00

100.

00.

0020

lm01

25l6

652

73.1

0946

-69.

9420

84.

3134

6415

.72

15.5

421

40.8

024

0.95

2-0

.013

-0.0

40.

0010

0.00

200.

0090

lm02

97n1

4819

75.2

1066

-67.

5588

4.31

8638

15.5

515

.26

1934

.637

70.

989

-0.0

21-0

.014

-0.0

010

-0.0

-0.0

030

lm04

67k1

8222

82.1

4873

-66.

0321

54.

3202

2415

.97

15.7

941

6.62

770.

97-0

.009

0-0

.031

0.0

-0.0

0.00

10lm

0187

m17

967

78.3

8296

-68.

8134

4.32

3013

16.2

716

.00

1579

.681

30.

97-0

.012

-0.0

4-0

.024

-0.0

14-0

.008

0lm

0467

n178

5082

.431

97-6

6.19

001

4.32

4035

15.9

415

.68

2309

.713

00.

968

0.0

-0.0

61-0

.001

0-0

.04

-0.0

lm02

05n1

7550

81.9

3375

-68.

6001

64.

3320

4116

.77

16.5

214

55.7

692

0.94

2-0

.004

0-0

.092

-0.0

070

-0.0

61-0

.006

0lm

0344

n907

483

.150

2-6

7.16

532

4.33

4821

14.7

814

.54

825.

8571

0.92

1-0

.011

-0.1

04-0

.005

0-0

.044

-0.0

010

lm05

77k2

2178

80.3

2518

-71.

684

4.33

6319

16.1

815

.97

2161

.771

80.

927

-0.0

24-0

.068

0.00

10-0

.003

00.

0060

lm03

31k2

2811

81.8

0895

-66.

3997

4.33

7633

15.0

914

.91

1355

.927

30.

926

-0.0

32-0

.085

-0.0

050

-0.0

210.

0050

lm00

91n3

2274

79.3

2109

-69.

3828

24.

3396

2815

.92

15.8

893

1.49

890.

967

-0.0

15-0

.032

0.00

10-0

.00.

0020

190


0211

k238

0383

.575

7-6

7.79

595

4.34

1552

15.7

215

.53

1116

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00.

973

-0.0

22-0

.018

0.0

0.00

200.

0060

lm03

17k2

1886

78.2

5325

-67.

4642

4.35

9786

14.8

414

.76

1935

.659

90.

929

-0.0

25-0

.086

-0.0

080

-0.0

220.

0050

lm03

44n1

1851

83.1

9611

-67.

1833

14.

4025

8515

.60

15.3

784

5.69

380.

99-0

.003

0-0

.012

0.0

-0.0

040

-0.0

010

lm03

37k2

5005

81.7

5818

-67.

4771

84.

4088

2215

.00

14.7

619

06.8

403

0.95

30.

0050

-0.0

67-0

.01

-0.0

390.

012

lm00

93m

1195

579

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73-6

9.46

628

4.42

2796

16.0

315

.87

1451

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60.

963

0.00

20-0

.057

-0.0

050

-0.0

33-0

.002

0lm

0292

l554

1*74

.122

64-6

6.79

039

4.44

2046

16.7

616

.58

2245

.621

60.

967

0.00

10-0

.05

-0.0

010

-0.0

320.

0020

lm00

34m

4602

*84

.663

94-6

9.80

398

4.45

4894

16.7

316

.80

2223

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80.

983

0.00

20-0

.022

-0.0

010

-0.0

16-0

.001

0lm

0290

m45

1074

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76-6

6.27

256

4.45

663

15.7

215

.58

382.

7421

0.87

3-0

.052

-0.1

41-0

.025

-0.0

520.

017

lm01

97m

2083

579

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83-6

8.83

562

4.48

8418

15.9

915

.78

397.

8481

0.99

4-0

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0-0

.012

-0.0

110.

00.

0040

lm00

90n2

0034

78.2

5898

-69.

3276

84.

5023

6315

.79

15.7

859

0.47

790.

978

0.00

10-0

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-0.0

22-0

.014

0.00

90lm

0021

l159

8582

.869

38-6

9.29

774

4.50

2779

14.8

314

.59

1082

.878

40.

867

-0.0

33-0

.175

-0.0

21-0

.057

0.00

60lm

0551

l214

1976

.056

41-7

0.73

615

4.50

3208

15.7

415

.52

837.

7661

0.98

-0.0

1-0

.019

-0.0

12-0

.006

0-0

.001

0lm

0243

m48

2489

.251

68-6

8.07

858

4.51

7961

15.8

415

.64

1987

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00.

964

-0.0

050

-0.0

46-0

.003

0-0

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-0.0

050

lm00

30l9

014

83.8

5675

-69.

2682

34.

5236

2215

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15.0

944

0.75

440.

967

-0.0

010

-0.0

39-0

.001

0-0

.019

-0.0

010

lm02

07m

1144

682

.147

97-6

8.77

459

4.52

6578

14.3

114

.03

741.

8064

0.86

70.

0010

-0.1

58-0

.007

0-0

.038

0.00

60lm

0182

n150

9977

.353

68-6

8.24

348

4.53

5109

15.5

915

.41

2263

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60.

983

-0.0

010

-0.0

17-0

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0-0

.003

0-0

.0lm

0283

m15

233

73.4

938

-66.

7020

54.

5408

4415

.45

15.1

517

83.7

591

0.93

3-0

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-0.1

15-0

.041

-0.0

750.

0020

lm00

21l1

5606

82.8

0078

-69.

2958

84.

5575

8115

.11

14.8

814

92.6

909

0.99

2-0

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0-0

.018

-0.0

040

-0.0

120.

0010

lm00

91l1

4577

78.9

1731

-69.

2871

94.

5666

5716

.40

16.5

917

91.7

729

0.96

3-0

.049

-0.0

67-0

.028

-0.0

43-0

.001

0lm

0027

n985

6*83

.481

8-7

0.31

804

4.56

889

17.2

917

.21

1883

.676

10.

947

-0.0

040

-0.0

860.

0020

-0.0

57-0

.003

0lm

0190

n218

6979

.392

04-6

7.93

565

4.57

1853

15.2

515

.04

2172

.765

80.

967

0.00

30-0

.043

-0.0

010

-0.0

240.

0020

lm01

14k1

9051

73.9

6926

-69.

8695

24.

5774

7115

.33

15.1

353

2.53

050.

873

-0.0

38-0

.152

-0.0

25-0

.054

0.00

10lm

0020

n196

1582

.673

97-6

9.32

445

4.58

5353

14.1

013

.94

754.

7607

0.90

9-0

.034

-0.0

92-0

.01

-0.0

080

-0.0

020

lm01

87m

1149

678

.387

39-6

8.77

464

4.59

1479

16.3

116

.07

1892

.839

00.

903

-0.0

9-0

.144

-0.0

42-0

.074

-0.0

020

lm00

33m

2170

085

.423

29-6

9.53

002

4.61

3339

15.1

915

.07

799.

8171

0.98

4-0

.005

0-0

.019

-0.0

050

-0.0

050

0.00

30lm

0133

n160

0071

.607

32-6

9.64

112

4.61

3573

16.4

216

.26

2305

.600

60.

994

-0.0

35-0

.018

0.00

10-0

.002

0-0

.004

0lm

0025

m30

936

83.3

2691

-69.

9173

74.

6368

4516

.37

16.3

510

92.6

860

0.89

1-0

.088

-0.1

39-0

.039

-0.0

680.

0080

lm02

11m

1885

9*83

.909

38-6

7.76

044

4.64

3221

916

.65

16.5

321

71.7

647

0.92

7-0

.011

-0.0

760.

0020

-0.0

080

-0.0

lm01

66m

2251

873

.367

13-6

8.84

454.

6587

9716

.63

16.4

918

11.7

418

0.98

50.

0020

-0.0

23-0

.008

0-0

.015

0.00

60lm

0550

k115

2375

.253

22-7

0.52

935

4.66

509

16.2

916

.02

1278

.541

50.

984

-0.0

060

-0.0

25-0

.006

0-0

.013

0.00

10lm

0185

n116

3678

.274

15-6

8.56

689

4.67

3342

16.3

716

.18

1255

.565

00.

946

-0.0

46-0

.068

-0.0

14-0

.031

0.00

20lm

0135

k140

0870

.902

69-6

9.83

939

4.67

4718

16.4

016

.38

737.

8651

0.97

7-0

.02

-0.0

20.

0020

0.00

100.

0010

lm03

50l4

429

84.4

6882

-66.

4321

84.

6868

9615

.42

15.2

720

09.6

418

0.98

1-0

.015

-0.0

160.

0010

0.00

300.

0030

lm01

35k9

012

71.2

563

-69.

8038

4.70

8726

16.2

216

.16

2254

.557

80.

992

-0.0

21-0

.011

-0.0

0.00

10-0

.002

0lm

0093

m30

768

79.3

3994

-69.

5646

74.

7211

5616

.56

16.4

214

40.8

605

0.90

9-0

.12

-0.1

35-0

.061

-0.0

880.

0060

lm02

25k1

8526

85.5

041

-68.

4653

24.

7506

9916

.19

16.0

115

47.7

200

0.97

6-0

.002

0-0

.01

-0.0

46-0

.006

0-0

.024

lm03

56m

1914

684

.794

8-6

7.43

387

4.75

5264

15.4

315

.22

2224

.790

30.

951

-0.0

020

-0.0

67-0

.011

-0.0

390.

0080

lm01

77m

1914

876

.591

68-6

8.82

087

4.76

0853

16.6

716

.48

802.

7677

0.98

1-0

.013

-0.0

25-0

.001

00.

0010

-0.0

010

lm05

51l2

0848

*76

.230

95-7

0.73

175

4.76

1963

615

.03

14.7

973

1.82

060.

986

-0.0

040

-0.0

16-0

.001

0-0

.004

00.

0lm

0333

n656

882

.251

58-6

6.78

851

4.77

0854

15.1

114

.84

1791

.790

80.

953

-0.0

22-0

.042

-0.0

010

0.00

200.

0050

lm05

43m

8169

74.5

4655

-70.

8411

44.

7778

6216

.01

15.7

619

26.6

584

0.94

9-0

.007

0-0

.078

-0.0

19-0

.044

0.00

90

191

lm01

80k1

6760

76.8

1278

-67.

7548

44.

7842

8815

.54

15.2

619

27.6

826

0.97

60.

0-0

.044

-0.0

070

-0.0

18-0

.004

0lm

0567

k232

5978

.473

29-7

1.64

955

4.80

3925

16.5

616

.38

1312

.507

90.

977

-0.0

27-0

.026

0.0

0.00

20-0

.004

0lm

0427

l127

6775

.272

-66.

1554

44.

8059

3216

.12

15.8

611

24.7

340

0.98

1-0

.006

0-0

.028

-0.0

010

-0.0

160.

0030

lm00

31n6

676

85.4

6572

-69.

2396

94.

8534

3115

.58

15.5

182

8.65

780.

954

0.00

50-0

.04

-0.0

14-0

.014

-0.0

070

lm02

94l2

5574

73.8

772

-67.

2727

44.

8554

5815

.50

15.3

219

47.6

718

0.97

1-0

.033

-0.0

370.

0030

0.0

-0.0

030

lm03

75l1

4140

89.0

3712

-67.

2052

54.

8706

5716

.50

16.3

680

6.73

110.

902

-0.0

87-0

.133

-0.0

49-0

.07

0.00

10lm

0311

n131

0878

.685

2-6

6.48

576

4.87

6315

15.6

315

.35

1569

.647

20.

962

-0.0

17-0

.068

-0.0

16-0

.055

-0.0

060

lm01

27k1

3132

73.1

4424

-70.

1884

4.89

2616

16.0

815

.96

1830

.667

30.

893

-0.0

61-0

.141

-0.0

38-0

.065

0.00

20lm

0216

l165

9082

.684

7-6

8.97

782

4.94

3171

15.9

315

.76

2263

.773

10.

981

-0.0

050

-0.0

25-0

.007

0-0

.015

-0.0

010

lm01

92n2

6066

*79

.022

75-6

8.31

199

4.94

5660

115

.38

15.3

139

7.84

810.

992

-0.0

060

-0.0

180.

0010

-0.0

090

-0.0

010

lm03

26n1

7046

*79

.460

31-6

7.56

801

4.95

1432

17.2

917

.07

1266

.556

30.

984

-0.0

050

-0.0

27-0

.006

0-0

.014

0.00

20lm

0476

k561

082

.743

42-6

5.94

116

4.95

1673

16.2

016

.09

1615

.591

90.

897

-0.0

12-0

.125

-0.0

1-0

.034

0.00

50lm

0344

l127

7382

.669

9-6

7.19

545

4.95

2487

15.4

315

.23

2095

.913

90.

980.

0050

-0.0

36-0

.004

0-0

.023

0.00

20lm

0185

l237

7277

.783

12-6

8.63

659

4.97

0047

15.7

315

.55

496.

6719

0.97

6-0

.023

-0.0

190.

0020

0.00

20-0

.001

0lm

0015

m26

793

81.5

8538

-69.

8949

74.

9706

0416

.08

15.8

411

93.6

422

0.96

8-0

.036

-0.0

170.

0020

0.00

200.

0020

lm01

21m

1164

273

.601

62-6

9.11

359

4.99

5179

15.4

615

.31

1153

.564

80.

877

-0.0

88-0

.171

-0.0

49-0

.079

0.01

7lm

0343

n257

4583

.953

7-6

6.91

106

4.99

707

14.6

914

.42

459.

7833

0.85

6-0

.033

-0.1

52-0

.017

-0.0

410.

014

lm01

12k2

2638

74.2

2448

-69.

5668

84.

9992

0714

.56

14.4

424

48.9

162

0.90

60.

0090

-0.0

430.

011

-0.0

25-0

.011

lm04

27k1

3855

75.5

5629

-66.

0060

55.

0164

6915

.86

15.6

222

10.7

725

0.91

-0.0

38-0

.088

-0.0

080

-0.0

250.

0060

lm03

45k8

617

83.8

0798

-67.

0097

85.

0195

5916

.20

15.9

420

85.9

135

0.99

6-0

.012

-0.0

050

-0.0

030

-0.0

040

0.00

40lm

0585

n191

26*

83.1

9272

-71.

4120

65.

0213

9217

.37

17.1

720

85.9

098

0.98

4-0

.0-0

.047

-0.0

060

-0.0

420.

0010

lm05

51m

1387

0*76

.504

67-7

0.53

596

5.03

2362

16.2

715

.91

1477

.654

80.

981

-0.0

080

-0.0

35-0

.008

0-0

.032

0.00

10lm

0224

k244

8784

.354

33-6

8.50

835.

0490

9715

.93

15.7

622

79.5

966

1.00

2-0

.008

0-0

.021

-0.0

040

-0.0

1-0

.0lm

0011

k236

3381

.126

98-6

9.18

929

5.08

3128

16.3

216

.37

2174

.779

40.

879

-0.0

66-0

.154

-0.0

36-0

.068

0.00

40lm

0093

k308

0579

.186

72-6

9.56

374

5.08

5768

16.3

916

.34

1900

.745

50.

9-0

.076

-0.1

46-0

.04

-0.0

73-0

.007

0lm

0012

n221

5180

.395

73-6

9.68

261

5.11

1026

16.6

416

.33

1082

.854

60.

966

-0.0

18-0

.03

0.00

100.

0030

0.00

40lm

0540

m13

587

73.4

6764

-70.

5342

15.

1180

7516

.11

15.8

019

42.6

161

0.98

3-0

.006

0-0

.024

-0.0

030

-0.0

170.

0lm

0355

l461

985

.475

74-6

7.13

673

5.13

2899

15.7

015

.53

1845

.848

60.

976

-0.0

3-0

.019

0.00

100.

00.

0060

lm01

23k2

357

72.8

2093

-69.

4152

5.15

6041

16.3

316

.32

2303

.603

80.

899

-0.0

76-0

.137

-0.0

42-0

.08

0.00

80lm

0191

l255

8979

.647

54-6

7.98

489

5.15

9253

15.6

715

.58

1745

.871

20.

886

-0.0

25-0

.12

-0.0

11-0

.03

0.00

90lm

0021

l307

7083

.060

41-6

9.37

757

5.17

1793

15.5

815

.37

1082

.878

40.

965

-0.0

16-0

.013

-0.0

76-0

.026

-0.0

34lm

0701

m12

218

81.9

3523

-71.

9413

25.

1720

2316

.45

16.4

516

24.5

706

1.00

4-0

.011

-0.0

060

0.00

100.

0010

-0.0

070

lm02

16k9

627

82.6

0651

-68.

7694

85.

2031

0614

.13

13.9

518

23.8

298

0.98

4-0

.014

-0.0

21-0

.0-0

.002

0-0

.001

0lm

0024

k279

7481

.698

32-6

9.80

184

5.20

4477

15.4

415

.32

1582

.644

10.

983

-0.0

17-0

.014

0.0

0.00

100.

0060

lm00

52n1

9538

88.2

6495

-69.

6868

85.

2254

415

.58

15.3

823

47.6

571

0.96

4-0

.019

-0.0

420.

0020

-0.0

020

0.00

20lm

0111

m91

7575

.643

76-6

9.09

596

5.25

5775

15.3

914

.99

1865

.594

10.

995

-0.0

070

-0.0

4-0

.002

0-0

.034

0.00

20lm

0100

m12

334

76.3

8395

-69.

1299

15.

2629

1216

.19

16.0

346

8.79

930.

896

-0.0

77-0

.141

-0.0

36-0

.072

0.00

80lm

0033

k756

985

.206

26-6

9.44

349

5.26

9115

.30

15.1

622

25.7

022

0.98

9-0

.004

0-0

.011

-0.0

040

-0.0

020

0.00

30lm

0333

l154

0481

.899

71-6

6.84

652

5.27

222

15.5

515

.42

2202

.780

80.

955

-0.0

19-0

.042

0.00

100.

0020

0.00

40lm

0612

l101

9487

.801

68-7

1.02

961

5.27

9445

16.4

516

.33

1547

.766

10.

991

-0.0

23-0

.012

-0.0

010

0.00

20-0

.001

0lm

0330

k429

080

.971

98-6

6.27

295

5.28

192

16.5

716

.43

1089

.819

30.

907

-0.0

98-0

.136

-0.0

49-0

.085

-0.0

020

192


0587

l185

0782

.383

94-7

1.78

632

5.28

2775

15.9

615

.80

383.

7489

0.91

3-0

.085

-0.1

33-0

.035

-0.0

77-0

.001

0lm

0223

l645

985

.372

76-6

8.18

986

5.29

9378

15.3

415

.20

845.

6984

0.92

2-0

.023

-0.0

74-0

.002

0-0

.008

00.

0080

lm01

16k2

1077

74.1

7121

-70.

2441

25.

3096

815

.40

15.1

922

50.5

707

0.97

2-0

.028

-0.0

28-0

.001

00.

0010

0.00

20lm

0207

k170

5981

.647

94-6

8.80

979

5.31

1128

16.2

216

.14

851.

7868

1.01

1-0

.064

-0.0

34-0

.027

-0.0

390.

0020

lm01

21n2

8673

73.6

5569

-69.

3697

45.

3272

8316

.05

15.9

416

10.5

479

0.89

5-0

.032

-0.1

18-0

.015

-0.0

360.

0090

lm00

20m

1635

982

.467

83-6

9.15

634

5.33

5197

14.9

914

.76

1794

.861

10.

933

-0.0

26-0

.105

-0.0

35-0

.053

-0.0

13lm

0224

m12

591*

84.9

7701

-68.

4286

75.

3449

314

.79

14.5

912

89.6

036

0.98

40.

0010

-0.0

32-0

.002

0-0

.029

-0.0

lm00

33m

6304

85.2

3578

-69.

4383

45.

3695

4515

.48

15.2

922

26.8

657

0.98

1-0

.006

0-0

.03

-0.0

050

-0.0

2-0

.001

0lm

0245

k709

5*89

.092

02-6

8.39

552

5.37

7706

16.8

616

.74

1773

.878

80.

978

-0.0

020

-0.0

35-0

.002

0-0

.01

0.00

10lm

0031

l229

8785

.196

81-6

9.34

126

5.41

3977

14.2

014

.06

1786

.789

00.

93-0

.007

0-0

.111

-0.0

050

-0.0

61-0

.001

0lm

0216

n105

8982

.753

61-6

8.92

483

5.44

858

14.8

414

.64

1255

.614

10.

977

-0.0

15-0

.026

-0.0

020

0.0

-0.0

020

lm00

92m

1877

478

.421

81-6

9.54

597

5.45

7309

15.7

315

.55

378.

7175

0.94

2-0

.008

0-0

.073

0.00

20-0

.048

0.00

40lm

0294

l138

1874

.125

05-6

7.19

756

5.47

1904

15.7

215

.55

1277

.498

10.

987

-0.0

1-0

.013

-0.0

010

0.00

100.

0010

lm01

14k2

1690

74.0

5789

-69.

8867

85.

5079

9515

.32

15.1

455

5.55

320.

947

0.00

30-0

.097

-0.0

28-0

.058

0.01

7lm

0223

k273

5385

.285

51-6

8.16

349

5.52

9928

16.2

016

.11

1191

.762

90.

991

-0.0

12-0

.006

0-0

.00.

0-0

.0lm

0186

m23

446

77.1

8403

-68.

8567

55.

5342

7416

.50

16.3

718

27.7

468

0.96

6-0

.026

-0.0

37-0

.003

0-0

.008

0-0

.002

0lm

0346

l134

3882

.817

42-6

7.54

852

5.57

0352

14.3

914

.16

837.

7814

0.91

-0.0

34-0

.078

-0.0

050

-0.0

10.

019

lm02

07n1

5251

81.9

3445

-68.

9611

55.

5988

4615

.47

15.2

012

52.5

839

0.99

-0.0

030

-0.0

13-0

.003

0-0

.008

00.

0lm

0093

k267

3279

.185

02-6

9.54

251

5.60

3447

15.8

815

.79

821.

7920

0.96

70.

0080

-0.0

590.

0020

-0.0

49-0

.008

0lm

0357

k240

43*

85.5

6601

-67.

4781

35.

6293

3616

.74

16.6

638

4.87

000.

922

-0.0

15-0

.085

-0.0

050

-0.0

160.

0070

lm00

24k1

6099

81.7

7809

-69.

7368

85.

6388

0615

.78

15.6

836

1.85

430.

926

-0.0

77-0

.105

-0.0

34-0

.063

-0.0

010

lm00

21k2

1280

82.7

5955

-69.

1804

55.

6718

4715

.60

15.6

516

28.5

730

0.94

9-0

.001

0-0

.051

-0.0

1-0

.016

-0.0

020

lm00

21m

2641

1*83

.246

68-6

9.20

468

5.70

8342

15.1

114

.95

1195

.705

70.

968

-0.0

010

-0.0

56-0

.001

0-0

.045

-0.0

010

lm01

85k1

5339

77.9

7996

-68.

4390

55.

7266

2716

.31

16.2

736

7.72

680.

898

-0.0

71-0

.133

-0.0

36-0

.062

0.00

50lm

0543

l281

5373

.870

45-7

1.11

878

5.73

6595

15.9

115

.88

556.

5493

0.97

9-0

.025

-0.0

160.

0010

-0.0

010

0.00

60lm

0127

l106

0873

.206

34-7

0.32

542

5.78

278

16.1

116

.00

1896

.734

90.

925

-0.0

13-0

.086

-0.0

020

-0.0

22-0

.001

0lm

0105

l584

276

.979

95-6

9.96

545.

7858

116

.12

16.0

022

30.8

260

0.97

60.

0020

-0.0

18-0

.048

0.00

300.

03lm

0091

n262

4779

.402

42-6

9.35

065.

8132

5615

.41

15.3

051

8.51

810.

983

-0.0

18-0

.013

0.0

0.0

0.00

30lm

0466

n117

1081

.642

73-6

6.13

484

5.82

2653

15.2

715

.05

1910

.725

80.

97-0

.016

-0.0

71-0

.015

-0.0

340.

0020

lm01

05l1

1377

*76

.822

83-7

0.01

872

5.83

6118

215

.37

15.1

914

16.8

380

0.98

3-0

.006

0-0

.022

-0.0

030

-0.0

060

0.0

lm00

13m

2077

681

.442

72-6

9.51

774

5.87

4426

16.2

916

.35

1114

.739

50.

942

-0.0

83-0

.095

-0.0

51-0

.065

0.00

10lm

0010

l242

4279

.898

64-6

9.36

666

5.94

1613

15.3

815

.20

1367

.872

70.

968

-0.0

12-0

.034

0.0

-0.0

010

0.00

40lm

0021

k148

3283

.109

98-6

9.13

885.

9732

4315

.36

15.1

641

1.80

040.

991

-0.0

040

-0.0

15-0

.007

0-0

.008

00.

0010

lm04

27n1

6272

*76

.031

68-6

6.18

205

6.00

374

15.2

414

.95

1208

.650

90.

963

-0.0

23-0

.042

0.00

100.

0-0

.003

0lm

0355

m22

531

85.6

2223

-67.

1003

96.

0534

5215

.49

15.3

318

45.8

486

0.98

2-0

.017

-0.0

1-0

.001

00.

0020

0.00

40lm

0220

l193

6884

.448

76-6

7.94

483

6.05

5055

16.0

715

.95

1560

.775

30.

935

-0.0

38-0

.076

-0.0

080

-0.0

16-0

.001

0lm

0171

n545

176

.178

42-6

7.84

531

6.06

5706

14.9

614

.77

1929

.635

90.

898

-0.0

54-0

.147

-0.0

36-0

.082

-0.0

010

lm03

56l1

5776

84.5

512

-67.

5715

6.07

2745

15.8

915

.79

809.

7491

0.98

7-0

.013

-0.0

080

0.00

200.

00.

0030

lm01

20k2

1262

*72

.106

59-6

9.19

104

6.12

7084

16.5

016

.42

1468

.577

80.

971

-0.0

050

-0.0

52-0

.006

0-0

.039

-0.0

lm02

11l6

920

83.3

0612

-67.

8407

26.

1912

116

.22

16.1

318

83.6

801

0.97

3-0

.018

-0.0

18-0

.0-0

.001

00.

0020

lm05

60n1

8929

77.5

3186

-70.

7122

16.

1926

9716

.23

16.0

220

28.5

055

0.97

9-0

.007

0-0

.024

-0.0

1-0

.016

-0.0

020

193

lm01

01k2

2147

76.8

8401

-69.

1909

36.

2082

4114

.74

14.5

314

42.7

940

0.97

4-0

.027

-0.0

26-0

.001

0-0

.001

00.

0030

lm00

20n6

294*

82.5

9216

-69.

2478

86.

2292

581

14.7

614

.42

875.

5657

0.95

50.

0050

-0.0

840.

0020

-0.0

72-0

.014

lm00

20n2

1732

*82

.663

34-6

9.33

662

6.27

1038

16.6

916

.52

596.

4752

0.98

90.

0010

-0.0

20.

0020

-0.0

140.

0010

lm05

64k2

1288

77.2

8653

-71.

2819

16.

3066

6315

.53

15.4

179

2.71

470.

89-0

.075

-0.1

42-0

.038

-0.0

640.

012

lm04

66n6

181

81.5

6648

-66.

0918

26.

3327

2315

.64

15.5

536

3.81

970.

91-0

.069

-0.1

1-0

.025

-0.0

470.

013

lm01

73n1

6894

76.4

0417

-68.

2482

16.

3479

4114

.97

14.7

053

8.54

950.

98-0

.002

0-0

.016

-0.0

150.

0010

-0.0

050

lm05

40k1

6892

*72

.737

25-7

0.56

097

6.37

983

16.6

016

.55

1117

.776

30.

982

-0.0

010

-0.0

3-0

.0-0

.013

-0.0

lm03

44k2

2660

82.6

3513

-67.

1089

76.

4348

2815

.04

14.8

411

93.6

830

0.96

9-0

.022

-0.0

270.

0010

0.00

10-0

.0lm

0124

k251

2672

.188

-69.

9129

36.

4383

5815

.64

15.5

886

4.68

420.

982

-0.0

16-0

.014

-0.0

010

0.00

10-0

.0lm

0303

k235

9976

.572

03-6

6.73

731

6.46

3085

15.5

915

.46

445.

7635

0.91

6-0

.041

-0.0

99-0

.013

-0.0

270.

0020

lm01

94n2

5484

79.0

1997

-68.

6558

26.

4734

6515

.36

15.2

210

98.6

948

0.95

3-0

.007

0-0

.053

-0.0

060

-0.0

220.

0070

lm00

90k1

5089

*78

.003

57-6

9.15

152

6.51

6940

116

.53

16.3

958

3.49

910.

987

-0.0

-0.0

290.

0030

-0.0

25-0

.003

0lm

0091

n319

44*

79.4

1439

-69.

3804

46.

5175

316

.79

16.7

572

7.87

060.

96-0

.012

-0.0

5-0

.006

0-0

.017

-0.0

lm03

46n1

7567

82.9

8578

-67.

5837

76.

5323

3214

.09

13.8

515

82.6

577

0.95

70.

0020

-0.0

52-0

.005

0-0

.018

-0.0

030

lm00

35m

2307

985

.593

5-6

9.88

483

6.56

9401

15.6

615

.50

862.

7340

0.96

1-0

.017

-0.0

410.

0020

0.00

10-0

.001

0lm

0690

k952

678

.102

79-7

1.90

847

6.59

6262

15.7

315

.50

508.

6562

0.97

7-0

.017

-0.0

21-0

.002

00.

0020

-0.0

010

lm04

57l1

3469

80.5

2857

-66.

1587

6.64

0871

15.1

714

.96

2263

.654

90.

905

-0.0

6-0

.131

-0.0

3-0

.069

-0.0

030

lm03

35n2

3069

82.4

8431

-67.

2425

6.89

8566

16.2

616

.07

1768

.846

80.

973

-0.0

43-0

.03

-0.0

020

-0.0

040

-0.0

020

lm01

80m

2716

4*77

.519

15-6

7.81

345

6.91

3797

915

.45

15.1

022

94.6

680

0.98

2-0

.008

0-0

.028

0.00

10-0

.018

0.00

30lm

0364

k127

5186

.121

86-6

7.04

148

6.97

7975

15.9

215

.78

705.

8406

0.95

3-0

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-0.0

41-0

.006

0-0

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00.

0050

lm02

94l4

906*

73.8

4732

-67.

1382

77.

0961

5415

.37

15.1

717

82.7

369

0.98

90.

0-0

.013

-0.0

010

-0.0

060

0.00

10lm

0335

n254

77*

82.2

8467

-67.

2884

17.

1173

239

14.9

314

.70

1834

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70.

91-0

.003

0-0

.093

-0.0

030

-0.0

210.

0020

lm02

14n1

4689

*82

.893

89-6

8.59

669

7.15

0098

15.0

715

.16

2270

.650

90.

991

-0.0

030

-0.0

090

-0.0

150.

0010

0.00

30lm

0367

m14

504*

87.6

0799

-67.

4051

7.17

7252

16.9

016

.79

2338

.653

30.

995

0.00

10-0

.017

0.00

100.

0-0

.0lm

0427

n121

2275

.865

53-6

6.14

977

7.19

4033

15.7

315

.45

1942

.626

50.

984

-0.0

080

-0.0

22-0

.03

-0.0

-0.0

12lm

0241

n189

6089

.434

26-6

7.93

432

7.22

7958

15.8

715

.72

402.

6331

0.97

8-0

.033

-0.0

220.

0010

0.00

10-0

.002

0lm

0246

k659

588

.145

96-6

8.74

102

7.28

4157

15.6

015

.50

2028

.543

90.

942

-0.0

78-0

.092

-0.0

29-0

.049

-0.0

020

lm00

93k5

253*

78.9

7127

-69.

4327

17.

2843

8815

.71

15.7

418

35.7

526

0.92

5-0

.039

-0.1

36-0

.02

-0.0

47-0

.002

0lm

0585

l584

282

.782

41-7

1.33

556

7.28

6296

14.9

514

.74

1102

.783

20.

967

-0.0

16-0

.026

0.0

-0.0

0.00

80lm

0033

m20

529

85.4

7251

-69.

5225

17.

4647

7814

.26

14.0

718

18.8

043

0.96

2-0

.002

0-0

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-0.0

030

-0.0

240.

0050

lm00

14k7

299

80.1

7669

-69.

7988

47.

5367

4715

.88

15.7

922

59.5

285

0.97

4-0

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-0.0

240.

00.

0010

0.00

10lm

0427

k750

5*75

.427

66-6

5.95

939

7.68

4446

15.4

015

.15

2192

.695

30.

981

-0.0

060

-0.0

15-0

.03

-0.0

010

-0.0

090

lm04

35m

1238

177

.556

51-6

5.62

774

7.69

6551

16.0

415

.88

1886

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80.

89-0

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-0.1

380.

0060

-0.0

490.

018

lm01

80n9

316

77.1

2842

-67.

9297

17.

7540

9615

.40

15.2

215

89.6

684

0.97

2-0

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-0.0

280.

0010

0.00

20-0

.0lm

0356

m11

102

84.7

4967

-67.

3777

77.

7883

515

.73

15.6

620

53.5

103

0.99

-0.0

26-0

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0.00

100.

0010

-0.0

030

lm00

33n1

2413

85.2

6999

-69.

6302

67.

9421

2615

.02

14.9

231

5.89

580.

974

0.00

70-0

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-0.0

1-0

.029

-0.0

11lm

0326

n774

379

.816

72-6

7.49

871

8.01

5506

15.6

915

.55

1896

.759

30.

929

-0.0

38-0

.116

-0.0

28-0

.046

0.00

50lm

0156

m35

36*

71.6

5461

-68.

8327

28.

2780

8616

.51

16.5

121

55.7

386

0.90

9-0

.013

-0.1

29-0

.006

0-0

.054

0.00

50lm

0157

m46

89*

72.5

8175

-68.

7322

98.

4029

4616

.44

16.4

041

1.71

140.

972

0.00

10-0

.021

-0.0

020

-0.0

060

-0.0

010

lm03

54n1

6185

*84

.837

11-6

7.21

527

8.45

8416

.06

15.9

514

97.7

810

0.97

2-0

.003

0-0

.03

-0.0

080

-0.0

2-0

.002

0lm

0020

k102

8781

.940

49-6

9.12

858.

4630

3914

.74

14.5

615

66.6

321

0.92

3-0

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01-0

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-0.0

440.

0010

194


0467

k119

17*

82.0

9084

-65.

9874

8.46

4606

315

.03

14.8

115

38.6

456

0.98

3-0

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0-0

.017

-0.0

050

-0.0

090

0.00

10lm

0024

m14

9882

.299

74-6

9.76

834

8.48

5941

15.0

714

.98

1447

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30.

915

-0.0

9-0

.145

-0.0

53-0

.099

0.00

30lm

0033

m59

6085

.302

16-6

9.43

568

8.58

3074

13.8

313

.63

2263

.784

60.

984

-0.0

030

-0.0

2-0

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-0.0

030

0.00

60lm

0356

l214

8684

.357

04-6

7.61

704

8.81

6562

15.6

915

.54

1657

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70.

887

-0.0

25-0

.122

-0.0

12-0

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0.01

4lm

0541

l927

5*73

.900

85-7

0.67

855

8.85

0098

16.5

516

.45

1926

.658

40.

980.

0010

-0.0

210.

0-0

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00.

0lm

0173

m17

717

76.5

4398

-68.

0953

18.

8565

3713

.59

13.3

919

18.6

627

0.97

6-0

.004

0-0

.027

-0.0

15-0

.007

00.

0030

lm01

91n3

246*

80.1

2526

-67.

8465

514

.645

028

15.4

515

.39

1150

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60.

986

-0.0

010

-0.0

17-0

.001

0-0

.003

00.

0010

lm01

73n3

2162

*76

.486

71-6

8.33

424

21.0

4149

214

.93

15.1

175

9.84

320.

957

-0.0

090

-0.0

86-0

.011

-0.0

16-0

.01

Tabl

eA

.1:

Iden

tifica

tion,

mai

npr

oper

ties

and

Four

ier

para

met

ers

for

1768

HEB

sin

the

LMC

(Col

umn

1:ER

OS-

2id

entifi

catio

nof

the

star

;C

olum

n2:

Rig

htas

cens

ion

from

the

ERO

S-2

cata

logu

e;C

olum

n3:

Dec

linat

ion

from

the

ERO

S-2

cata

logu

e;C

olum

n4:

Perio

d(∗

-Sta

rsfo

rwhi

cha

new

perio

dw

asde

rived

inth

isst

udy.

See

text

fort

hede

tails

.);C

olum

n5:

Mea

nm

agni

tude

inth

eR

EROS

pass

band

;Col

umn

6:M

ean

mag

nitu

dein

the

BEROS

pass

band

;C

olum

n7:

Epoc

hof

the

prim

ary

min

imum

;C

olum

n8-

Col

umn

14:

Four

ierp

aram

eter

sof

the

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220

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